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Math Help - Green's Theorem problem

  1. #1
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    Green's Theorem problem

    ∫c (x^2+y^2)dx + (x^2+y^2)dy , C is defined by y=x , y=(1/6)x^2 , 0<x<6

    For the limits I'm doing dydx, so:
    y is from 0 to x
    x is from 0 to 6

    ∫c (x^2+y^2)dx + (x^2+y^2)dy
    = ∫∫2x-2y dydx = 2xy-y^2 from 0 to x
    = ∫x^2 dx = (1/3)x^3 from 0 to 6 = 72.

    I got it wrong... what did I do wrong and what is the correct answer?



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  2. #2
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    Re: Green's Theorem problem

    The limits are actually \displaystyle \begin{align*} 0 \leq x \leq 6 \end{align*} and \displaystyle \begin{align*} \frac{1}{6}x^2 \leq y \leq x \end{align*}.
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  3. #3
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    Re: Green's Theorem problem

    Thank you! I keep forgetting how the limits work for multivariable integration...
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    Re: Green's Theorem problem

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