Math

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Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot !

1) For the green's theorem,

Q: Using Green's theorem, evaluate the line integral F(r).dr counterclockwise around the boundary C of the region R, where: F = (x lny)i + (y e^x)j, R the rectangle 0<=x<=3, 1<=y<=2

I got the answer : 27.552. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.


2) I'm totally unsure about finding the surface integral. How do I know the shape of the surface ?

Q: Evaluate surface integral ff(double integral sign)G(r)dA where G(x,y,z)= xe^y + x^2z^2, S: x^2 + y^2 = a^2, y>=0, 0<=z<=h


3) and finding the curl function f
Q: Find a function f such that grad f = F.

All I know is, it has something to do with curl. Something like F = grad f. How do I find the function ?


Thanks again !

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