# 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?

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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
Homework Helper
Gold Member
But I can't. Because sin(x+pi)-sin(x)=sin(x)+sin(pi)-sin(x)=sin(pi)=0. The integral of 0 is?
$\sin(a+b)\ne \sin a +\sin b$

Because sin(x+pi)=sin(x)+sin(pi)
That is most certainly not correct. Can you check your compound angle formula?

Then what's sin(a+b)?

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