I have to verify Green's theorem for a question with the region being a parallelogram with vertices $(0,0), (1,1),(2,0),(3,1) $ and I'm having trouble with the standard approach of finding limits of integration with Fubini’s Theorem. Now here is where I'm having the problem.

I know that if I'm integrating first with respect to y and then with respect to x, I have to draw a vertical line cutting through the region R in the direction of increasing y and the upper and lower cuts mark the corresponding limits of y as functions of x. I have found x limits to be from 0 to 2 but I'm having a lot of trouble with limits of y.

It seems like the line enters at $y = 0$ and leaves at $y = 1 $. How do you write them as functions of x? Thank you.

I have uploaded a picture to show my attempt and where I got stuck. My attempt


It is something like,

$$\int_{y=0}^{1}\int_{y}^{y+2} \left(...\right)dxdy$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.