MATLAB® Test Report
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Timestamp: |
25-Jul-2025 17:34:59 |
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Host: |
pkrvmpptgkbjq6m |
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Platform: |
glnxa64 |
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MATLAB Version: |
24.1.0.2837808 (R2024a) Update 7 |
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Number of Tests: |
5 |
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Testing Time: |
31.9185 seconds |
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Overall Result: |
PASSED |
Overview
/home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/
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19.8366 seconds |
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1.5412 seconds |
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10.5407 seconds |
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Details
/home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/
SmokeTests
SmokeRun
Class Setup Parameters: Project=matlab.project.Project
Test Parameters: File=LineIntegrals.mlx
The test passed. Duration: 19.8366 seconds
Events:
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:39 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_a249bba6-4f97-4922-b7f2-c87ba50b177b.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:41 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_8c3691b9-1981-42b5-9008-d693e9a937ff.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:41 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_689c1ad4-fa58-4933-b4b3-ccc29dbd46bc.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:42 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_0e3e5038-30ca-4ce8-9cc0-7d3a12816b29.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:42 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_c6a91eb1-cca4-4cb7-b169-ff4aaef8014b.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:43 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_fda3d2fb-8725-4ca6-9058-2f97c4cbd98b.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:43 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_a35bdf1c-a82b-4b07-b786-c783865d17fc.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:43 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_f301687f-d59c-428c-b5ed-14bd38c96092.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:43 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_f0138e1d-eaaf-4f55-bae0-98d86d8ba594.png
Event Location: SmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SmokeTests.m (SmokeTests.SmokeRun) at 94 |
(Overview)
FunctionTests
testPlotWithValidNonDefaultInputs
The test passed. Duration: 1.2492 seconds
Events:
Verification passed.
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Framework Diagnostic: verifyNotEmpty passed. --> The value has a size of [1 1]. Actual Value: Axes (Test Plot) with properties: XLim: [5 11] YLim: [-6 6] XScale: 'linear' YScale: 'linear' GridLineStyle: '-' Position: [0.130000000000000 0.110000000000000 0.775000000000000 0.815000000000000] Units: 'normalized' Use GET to show all properties Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 22 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "X-axis" Expected Value: "X-axis" Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 23 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "Y-axis" Expected Value: "Y-axis" Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 24 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "Z-axis" Expected Value: "Z-axis" Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 25 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "Test Plot" Expected Value: "Test Plot" Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 26 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The numeric values are equal using "isequaln". Actual Value: 4 Expected Value: 4 Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 27 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The numeric values are equal using "isequaln". Actual Value: 9 Expected Value: 9 Event Location: FunctionTests/testPlotWithValidNonDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithValidNonDefaultInputs) at 28 |
(Overview)
testPlotWithDefaultInputs
The test passed. Duration: 0.2919 seconds
Events:
Verification passed.
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Framework Diagnostic: verifyNotEmpty passed. --> The value has a size of [1 1]. Actual Value: Axes (Curve) with properties: XLim: [4.250000000000000 11.750000000000000] YLim: [-5.124984265959235 6.124858393633110] XScale: 'linear' YScale: 'linear' GridLineStyle: '-' Position: [0.130000000000000 0.110000000000000 0.775000000000000 0.815000000000000] Units: 'normalized' Use GET to show all properties Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 42 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "X" Expected Value: "X" Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 43 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "Y" Expected Value: "Y" Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 44 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "Z" Expected Value: "Z" Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 45 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The strings are equal. Actual Value: "Curve" Expected Value: "Curve" Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 46 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The numeric values are equal using "isequaln". Actual Value: 1 Expected Value: 1 Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 47 |
Verification passed.
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Framework Diagnostic: verifyEqual passed. --> The numeric values are equal using "isequaln". Actual Value: 10 Expected Value: 10 Event Location: FunctionTests/testPlotWithDefaultInputs Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/FunctionTests.m (FunctionTests.testPlotWithDefaultInputs) at 48 |
(Overview)
SolnSmokeTests
ExistSolns
Class Setup Parameters: Project=matlab.project.Project
Test Parameters: File=LineIntegrals.mlx
The test passed. Duration: 0.0660 seconds
(Overview)
SmokeRun
Class Setup Parameters: Project=matlab.project.Project
Test Parameters: File=LineIntegrals.mlx
The test passed. Duration: 10.4747 seconds
Events:
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:54 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_9ab61e2b-33f8-40d4-9481-171291a86103.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:55 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_de606800-bae0-4995-8081-76f25a7365af.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:55 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_d2e397ae-ab25-40a6-8b13-7bbc53e1ebd9.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:55 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_d047cc75-a5b1-4427-b44a-71ac00ea4318.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:56 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_cce42702-9c9e-420d-ad26-dee918ed8f7f.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:56 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_92a6dbfe-783c-4ac3-a18d-6c9f75f55562.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:56 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_0d23c6fd-ccd4-4d36-a00e-48a11b115eba.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:56 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_c377a9ae-db15-44f7-ba8d-eb55e28d3ff5.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:56 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_9242a92a-acdc-46f7-a3dc-ce2495db1054.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
Diagnostic logged.
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Timestamp: 25-Jul-2025 17:34:56 Verbosity: Terse Logged Diagnostic: Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_025c45bf-cb6f-4d11-92b6-7d47fa9700a7.png
Event Location: SolnSmokeTests[Project=matlab.project.Project]/SmokeRun(File=LineIntegrals.mlx) Stack: In /home/runner/work/Multivariable-Integrals/Multivariable-Integrals/SoftwareTests/SolnSmokeTests.m (SolnSmokeTests.SmokeRun) at 110 |
(Overview)
Command Window Text
Running SmokeTests >> Running LineIntegrals.mlx Please select a curve. You must select a curve to determine a line integral. a) is not correct. What is the curl of F_vec == (x - 3)*e_y? What is the curl of y*sin(x)*e_x - y*cos(x)*e_y? Alternately, can you compute a G with gradient(G) == y*sin(x)*e_x - y*cos(x)*e_y? Please correct your reasoning and try again. The curve C is a straight line from (4,-4) to (0,-4) and F_vec == e_r or, equivalently, F_vec == (x/sqrt(x^2 + y^2))*e_x + (y/sqrt(x^2 + y^2))*e_y. This is the default value. Please solve the problem. The value -999 is not correct. That is the default value. Please try again. The value -999 is not correct. That is the default value. Please try again. The value -999 is not correct. That is the default value. Please try again. The value -999 is not correct. That is the default value. Please try again. The value -999 is not correct. That is the default value. Please try again. Edge 1:int(- 0.5902*x - 2.049, x, 5.0, 0.358) == 16.8508 Edge 2:int(1.1323*x - 2.6654634, x, 0.358, -3.2102) == 15.2725 Edge 3:int(3.1692*x + 3.87336584, x, -3.2102, -1.4563) == -6.1758 Edge 4:int(- 0.3344*x - 1.22898672, x, -1.4563, -6.984) == -1.0064 Edge 5:int(0.371*x + 3.697264, x, -6.984, -2.6967) == 8.152 Edge 6:int(2.6955*x + 9.96565485, x, -2.6967, -1.1062) == 7.6989 Edge 7:int(- 2.3054*x + 4.43376652, x, -1.1062, 1.0388) == 9.677 Edge 8:int(0.2226*x + 1.80756312, x, 1.0388, 6.3004) == 13.809 Edge 9:int(0.7025*x - 1.215831, x, 6.3004, 1.4125) == -7.2987 Edge 10:int(- 1.3314*x + 1.6569025, x, 1.4125, 5.0) == -9.3699 The area of the star is the sum total: 47.6094 CorrectSoln = 123/2 That is the default value. The area is positive. Work = -88*log(8/5) which is approximately -41.3603 kJ. Because the work is negative, this means that we must put energy into the system to compress the cylinder. [Terse] Diagnostic logged (2025-07-25 17:34:39): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_a249bba6-4f97-4922-b7f2-c87ba50b177b.png [Terse] Diagnostic logged (2025-07-25 17:34:41): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_8c3691b9-1981-42b5-9008-d693e9a937ff.png [Terse] Diagnostic logged (2025-07-25 17:34:41): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_689c1ad4-fa58-4933-b4b3-ccc29dbd46bc.png [Terse] Diagnostic logged (2025-07-25 17:34:42): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_0e3e5038-30ca-4ce8-9cc0-7d3a12816b29.png [Terse] Diagnostic logged (2025-07-25 17:34:42): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_c6a91eb1-cca4-4cb7-b169-ff4aaef8014b.png [Terse] Diagnostic logged (2025-07-25 17:34:43): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_fda3d2fb-8725-4ca6-9058-2f97c4cbd98b.png [Terse] Diagnostic logged (2025-07-25 17:34:43): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_a35bdf1c-a82b-4b07-b786-c783865d17fc.png [Terse] Diagnostic logged (2025-07-25 17:34:43): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_f301687f-d59c-428c-b5ed-14bd38c96092.png [Terse] Diagnostic logged (2025-07-25 17:34:43): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_f0138e1d-eaaf-4f55-bae0-98d86d8ba594.png . Done SmokeTests __________ Running FunctionTests .. Done FunctionTests __________ Running SolnSmokeTests .>> Running LineIntegralsSoln.mlx Yes, the integral of a radially outward field over this clockwise rectangle is visibly zero. This does require observing that the radially outward field is conservative. You are correct. Options b), c), and d) are conservative while a) and e) are not conservative. a) (curl(F_vec) == e_z) ~= 0 so F_vec is not conservative. b) G == -cos(x) - y^3/3 so F_vec is conservative. c) G == (-3)/r^2 so F_vec is conservative. d) G == (2*x - 3*y) + z s F_vec is conservative. e) (curl(F_vec) == (y - 1)*sin(x)*e_z) ~= 0 so F_vec is not conservative. The curve C is a straight line from (-2,-3) to (5,4) and F_vec == x*e_x. The curve is a straight diagonal line. C can be parameterized as s(t) = (x(t),y(t)) with x(t) == 7*t - 2 and y(t) == 7*t - 3 for (0 <= t) <= 1. This means that ds/dt = (7,7). Note that in this case, the field can be parameterized as F_vec == (7*t - 2)*e_x. So the problem becomes: int(49*t - 14, t, 0, 1) == 21/2 This answer is correct. This answer is correct. This answer is correct. This answer is correct. The value 1.5 is not correct. Please try again. Edge 1:int(- 0.3341*x - 0.6636, x, 4.0, 0.4167) == 5.0215 Edge 2:int(3.3427*x - 2.19570309, x, 0.4167, -0.666) == 2.8288 Edge 3:int(- 2.634*x - 6.176544, x, -0.666, -1.6926) == 3.1518 Edge 4:int(- 0.3624*x - 2.33189824, x, -1.6926, -4.4116) == 3.333 Edge 5:int(0.4428*x + 1.22035648, x, -4.4116, -1.2944) == -0.1339 Edge 6:int(- 4.3364*x - 4.96583616, x, -1.2944, -2.0605) == -1.7682 Edge 7:int(- 1.1151*x + 1.67153645, x, -2.0605, 0.2155) == 6.1456 Edge 8:int(0.6005*x + 1.30169225, x, 0.2155, 3.1382) == 6.7473 Edge 9:int(1.424*x - 1.2825968, x, 3.1382, 1.0197) == -3.5544 Edge 10:int(- 0.7279*x + 0.91173963, x, 1.0197, 4.0) == -2.7277 The area of the star is the sum total: 19.0438 Edge 1:int(0.6*x - 3.4, x, 4.0, -1.0) == 12.5 Edge 2:int(- 1.6667*x - 5.6667, x, -1.0, -4.0) == 4.5 Edge 3:int(0.6*x + 3.4, x, -4.0, 1.0) == 12.5 Edge 4:int(4.0*x, x, 1.0, 0) == -2.0 Edge 5:int(-0.25*x, x, 0, 4.0) == -2.0 The area of the star is the sum total: 25.5 CorrectSoln = 51/2 Work = -88*log(8/5) which is approximately -41.3603 kJ. Because the work is negative, this means that we must put energy into the system to compress the cylinder. [Terse] Diagnostic logged (2025-07-25 17:34:54): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_9ab61e2b-33f8-40d4-9481-171291a86103.png [Terse] Diagnostic logged (2025-07-25 17:34:55): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_de606800-bae0-4995-8081-76f25a7365af.png [Terse] Diagnostic logged (2025-07-25 17:34:55): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_d2e397ae-ab25-40a6-8b13-7bbc53e1ebd9.png [Terse] Diagnostic logged (2025-07-25 17:34:55): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_d047cc75-a5b1-4427-b44a-71ac00ea4318.png [Terse] Diagnostic logged (2025-07-25 17:34:56): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_cce42702-9c9e-420d-ad26-dee918ed8f7f.png [Terse] Diagnostic logged (2025-07-25 17:34:56): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_92a6dbfe-783c-4ac3-a18d-6c9f75f55562.png [Terse] Diagnostic logged (2025-07-25 17:34:56): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_0d23c6fd-ccd4-4d36-a00e-48a11b115eba.png [Terse] Diagnostic logged (2025-07-25 17:34:56): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_c377a9ae-db15-44f7-ba8d-eb55e28d3ff5.png [Terse] Diagnostic logged (2025-07-25 17:34:56): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_9242a92a-acdc-46f7-a3dc-ce2495db1054.png [Terse] Diagnostic logged (2025-07-25 17:34:56): Figure saved to: --> /tmp/4a671c2f-a11c-439b-9954-c7a184072a32/Figure_025c45bf-cb6f-4d11-92b6-7d47fa9700a7.png . Done SolnSmokeTests __________