Homework Help: How to integrate this?

1. Jan 24, 2015

Math10

1. The problem statement, all variables and given/known data
How to integrate the double integral cos(x+y) dy dx from 0 to pi and from 0 to pi again.

2. Relevant equations

3. 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?

2. Jan 24, 2015

LCKurtz

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

3. Jan 24, 2015

Fightfish

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

4. Jan 24, 2015

Math10

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

5. Jan 24, 2015

LCKurtz

$\sin(a+b)\ne \sin a +\sin b$

6. Jan 24, 2015

Fightfish

That is most certainly not correct. Can you check your compound angle formula?

7. Jan 24, 2015

Math10

Then what's sin(a+b)?

8. Jan 24, 2015

Fightfish

9. Jan 24, 2015

Math10

@Fightfish , thank you so much for the info! I got it!