# Thread: Double integrals, reversing the order of integration.

1. ## Double integrals, reversing the order of integration.

Hi, I have been told to integrate the double integral sec x dx dy with the limits 0<y<1 and 0<x<cos^-1 y by first reversing the order of integration.

The problem I am having is I can't quite understand yet how to alter these limits.

I tried to change them and ended up with 0<y<cos x and cos^-1y < x < 0

After trying to integrate with these new limits I was stumped when trying to work out y sec (cos x) - y sec 0.

Any help would be greatly appreciated, thanks, Martin.

2. ## Re: Double integrals, reversing the order of integration.

Originally Posted by mgrafton
Hi, I have been told to integrate the double integral sec x dx dy with the limits 0<y<1 and 0<x<cos^-1 y by first reversing the order of integration.

The problem I am having is I can't quite understand yet how to alter these limits.

I tried to change them and ended up with 0<y<cos x and cos^-1y < x < 0

After trying to integrate with these new limits I was stumped when trying to work out y sec (cos x) - y sec 0.

Any help would be greatly appreciated, thanks, Martin.
Just to clarify, your integral is

$\displaystyle \int_{0}^{1}\int_{0}^{\cos^{-1}(y)}\sec(x)\,dx\,dy.$

Is that correct?