Green's Theorem, how do i set up the integration structure with this problem?

[kyle_can]

Sorry new to the whole Green's Theorem. Usually I'm given separate Q and P functions. What do I do with that F? Ok I do have the dimensions for a rectangle. I think it's best to split into half into two rectangles. The limits for integration are 1 to 1.5 for x and 0 to 3 for y for the first half then 1.5 to 3 for x and 0 to 3 for y for the second integration. Hmmm but what function do I integrate? Am I supposed to split the F into P and Q? How would the overall form look? I can do the integration out myself but I don't know how to set it up. Thanks!

 

[HallsofIvy]

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Sorry new to the whole Green's Theorem. Usually I'm given separate Q and P functions. What do I do with that F? Ok I do have the dimensions for a rectangle. I think it's best to split into half into two rectangles. The limits for integration are 1 to 1.5 for x and 0 to 3 for y for the first half then 1.5 to 3 for x and 0 to 3 for y for the second integration. Hmmm but what function do I integrate? Am I supposed to split the F into P and Q? How would the overall form look? I can do the integration out myself but I don't know how to set it up. Thanks!

Do you have difficulty reading the problem? The statement of Green's Theorem in the problem itself says that $\displaystyle \vec{F}= M\vec{i}+ N\vec{j}$ and then has $\displaystyle \int\int \left(\frac{\partial N}{\partial y}- \frac{\partial M}{\partial x}\right) dxdy$. "P" and "Q" are called "M" and "N" here.

What is special about x= 1.5 that you would want to split the integral there? And why to x= 3? The x values are from x= 1 to x= 5.