# What am I doing wrong when solving this Green's theorem problem?

1. Dec 6, 2013

### ainster31

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

$$Q=x\quad P=y^2-2y\\\oint_C{Pdx+Qdy}\\=\int_{C1}(y^2-2y)dx+xdy+\int_{C_2}(y^2-2y)dx+xdy\\=\int_{-\pi/2}^{\pi/2}(((sint+1)^2-2(sint+1))(-sint))dt+cost(cost)dt\\=\int_{-\pi/2}^{\pi/2}(2sin^2t+4sint+2)\\=3\pi$$

Correct answer is $\pi/2$.

2. Dec 7, 2013

### njoysci

Everything is fine except going from second to last step from your answer to the following step.
Integral should be of (- (sint)^3 + sint + (cost)^2) dt
This will give you the correct answer.