What is the Circulation of F Around C Using Green's Theorem?

[sunnyday11]

Homework Statement

F(x,y) = y i + (x²y + exp(y²)) j
Curve C begin at point (0,0) go to point (pi, 0) along the straight line then go back to (0,0) along curve y=sin(x)

Find circulation of F around C

Homework Equations

The Attempt at a Solution

Curve part 1

Using Green theorem I got

$$\int$$$$^{0}_{0}$$$$\int$$$$^{pi}_{0}$$$$_{R}$$ (2xy-1) dxdy

= 0 since y was from 0 to 0

I got stuck on the second parameterization. I know y=sin(x) but y still moves from 0 to 0 giving a result of 0 and this does not make any sense.

Thank you!

 

[Sethric]

The integral should be over the region bounded by the curve. You don't need to parametrize the line unless you intended to do the line integral side. Since you already took the curl, I assume you are doing the bounded region side. Therefore, the bounds of your integral need to be the bounds of the region. Try to find a formula for y that bounds the upper part of the region.