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# Solved Problems-14

Problem-14
Compute the line integral of  along the triangular path shown in the figure.
Line integral
Solution
Here,

The closed line integral is given as,

Along the path AB, dx = dz = 0, x = z = 0; y varies from 0 to 1.

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,
Line integral along ABC

Along the path CA, dx = dy = 0, x = y = 0; z varies from 2 to 0.

By addition, we get the closed line integral as,