Evaluate integral using Green Theorem

daphnelee-mh · Jul 3, 2020

Handwritten work: a sketch of the triangle bounded by x = 1, y = 1 and y = x - 1 with vertices (1,1), (2,1), (1,0), then Green's theorem double integral of e^(y^2) over that region, written as integral from 1 to 2 of integral from 0 to x-1 of e^(y^2) dy dx.

I got stuck here, how to integrate e^(y^2), I searched but it's something like error function

WWGD · Jul 3, 2020

Try changing the order of integration.

WWGD · Jul 3, 2020

But you usually parametrize the curve along which you integrate. Edit: Change the limits of integration accordingly when you change the order of integration. These limits should be a function of y alone and not of x. Does that work?

daphnelee-mh · Jul 3, 2020

WWGD said:

But you usually parametrize the curve along which you integrate. Edit: Change the limits of integration accordingly when you change the order of integration. These limits should be a function of y alone and not of x. Does that work?

Handwritten derivation applying Green's theorem to a line integral over a clockwise curve, with a double integral over a region, change of integration order, substitution u = y^2, and final result 1/2(1 - e^5).

I got this answer after changed the integrating order

WWGD · Jul 3, 2020

daphnelee-mh said:

View attachment 265800
I got this answer after changed the integrating order

Looks right. Do you have a way of checking? Maybe Wolfram?

daphnelee-mh · Jul 3, 2020

I checked it using Mathway just now, it's correct, thank you.

Evaluate integral using Green Theorem

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