I'm stuck on how to change the order of integration for this question,
$$\int_0^{2\pi} \int_{\cos x}^1\, f(x,y)\,\,\,dydx $$
We know that if we take vertical strips of the original integral the boundaries are
$\cos x \le y \le 1$
$0 \le x \le 2\pi$
Which is easy to integrate for, the answer being $2\pi$. However I am unsure how to obtain the boundaries for the horizontal strips through changing the order of integration.
I suspect that we have $-1 \le y \le 1$ for the y terminals but uncertain for the x terminals. Am I right in setting the y terminals to this?
The final answer by either taking horizontal or vertical strips should be $2\pi$
Any suggestions would be appreciated :)
I suggest you sketch the curves $y = \cos x$ and $y=1$.
Now, draw a horizontal line across this region. How would you express the endpoints in terms of y?