Evaluate the line integral
$3xy^2dx+8x^3dy$ where $C$ is the boundary of the region between the circles $x^2+y^2=1$ and $x^2+y^2=64$ having positive orientation.
Okay so I first looked at the first circle. I took $x=\cos t$ and $y=\sin t$. $dx=-\sin t dt$ and $dy=\cos t dt$
I looked at the second circle. I took $x=8\cos t$ and $y =8\sin t$. Then $dx = -8\sin t dt$ and $dy = 8\cos t dt$.
I looked up how to solve these kinds of problem and so I solved it two ways. First I plugged it into $A = (1/2)$ the integral of $xdy + ydx$. I then subtracted $A2-A1$ but I got $63\pi$. Lon capa said this was incorrect. Then I plugged it into the $f(x,y)$ equation that the problem gave me. However lon capa said that was incorrect as well... Please can someone tell me what I'm doing wrong?