Question

**Will Medal**
Calc 3
Can someone help me go through this problem please

Answer 1

@ganeshie8

Answer 2

I understand what to do if there is one circle but not two

Answer 3

Have you tried parameterizing? First break up the whole path into sub-paths. (see sketch)

Let \(x=2\cos t\) and \(y=2\sin t\) for the larger circle (radius 2) and \(x=\cos t\) and \(y=\sin t\) for the smaller circle (radius 1). The paths along the axes are straightforward (literally), so you can set \(x=0\) for the vertical line and \(y=0\) for the horizontal one.

Answer 4

Whoops, forgot my labels:
So you have
\[\begin{align*}I&=\int_C(4+e^{\cos x})\,dx+(\sin y+3x^2)\,dy\\\\
&=\int_{C_1}(\cdots)+\cdots+\int_{C_4}(\cdots)
\end{align*}\]