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Use Green’s Theorem to evaluate the integral H C x ln ydx where C is the...

Use Green’s Theorem to evaluate the integral H C x ln ydx where C is the positively oriented boundary curve of the region bounded by x = 1, x = 2, y = e^x and y = e^(x^2) .

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Answer #1

Here, we need to find the line integral of the function around the path shown in the figure below.

Given, there is positively oriented boundary curve.

The Green's theorem and the solution is shown below:

Hence , the value of the integral is 17/12 = 1.41667

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