# 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!