Thread: how to switch parameters for double integrals

1. how to switch parameters for double integrals

This is probably very simple but I don't know why I am having trouble switching the order of integration and the parameters for double integrals.

For example,

if the x parameters are 0 and pi and the y parameters are 0 and sinx,

how would i change the parameters so I express x as function of y and get two values for y boundaries

2. The double integral

$\int_0^{\pi}\int_0^{\sin x}dy\,dx$

is equivalent to

$\int_0^1\int_{\arcsin y}^{\pi-\arcsin y}dx\,dy.$

Note that as $x$ passes $\pi/2$, our formula for the inverse changes.

3. Is there any other way this can be done without using arcsin?

4. Originally Posted by messianic
Is there any other way this can be done without using arcsin?
Since y = sin x is one of the curves bounding the region the answer to your question is obviously no!