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

  1. Dec 6, 2013 #1
    1. The problem statement, all variables and given/known data

    gihQcn6.png

    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. jcsd
  3. Dec 7, 2013 #2
    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.
     
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