# Math Help - Green's Theorem problem

1. ## 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?

2. ## 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*}.

3. ## Re: Green's Theorem problem

Thank you! I keep forgetting how the limits work for multivariable integration...