How to integrate this?

Homework Statement

How to integrate the double integral cos(x+y) dy dx from 0 to pi and from 0 to pi again.

The Attempt at a Solution

Here's the work:
u=x+y
du=dy
cos(u)du=sin(x+y)
integral of [sin(x+y)] evaluate from 0 to pi dx from 0 to pi
integral of (sin(x+pi)-sin(x))dx from 0 to pi
And what's next?

LCKurtz
Homework Helper
Gold Member

Homework Statement

How to integrate the double integral cos(x+y) dy dx from 0 to pi and from 0 to pi again.

The Attempt at a Solution

Here's the work:
u=x+y
du=dy
cos(u)du=sin(x+y)
integral of [sin(x+y)] evaluate from 0 to pi dx from 0 to pi
integral of (sin(x+pi)-sin(x))dx from 0 to pi
And what's next?

Integrate again, similar to what you did for the first integral.

Er...doesn't the final step that you list give you the answer already?

But I can't. Because sin(x+pi)-sin(x)=sin(x)+sin(pi)-sin(x)=sin(pi)=0. The integral of 0 is?

LCKurtz