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Solved Problems-14

Compute the line integral of Description: 81550.png along the triangular path shown in the figure.
Description: 81541.png
Line integral 
Here, Description: 81527.png
Description: 81517.png
Description: 81510.png
The closed line integral is given as,
Description: 81502.png
Along the path AB, dx = dz = 0, x = z = 0; y varies from 0 to 1.
Description: 81484.png
Along the path BC, dx = 0, x = 0; y varies from 1 to 0 and z varies from 0 to 2.
Also, for this path, the equation relating y and z is obtained as,
Description: 81476.png
Description: 81468.png
Description: 101684.png
 Line integral along ABC
Along the path CA, dx = dy = 0, x = y = 0; z varies from 2 to 0.
Description: 81459.png
By addition, we get the closed line integral as,
Description: 81452.png

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