Homework Help: How to integrate this?

Math10 · Jan 24, 2015

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
The answer is -4.

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?

LCKurtz · Jan 24, 2015

Math10 said: ↑

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
The answer is -4.

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?

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

Fightfish · Jan 24, 2015

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

Math10 · Jan 24, 2015

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 · Jan 24, 2015

Math10 said: ↑

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##

Fightfish · Jan 24, 2015

Math10 said: ↑

Because sin(x+pi)=sin(x)+sin(pi)

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

Math10 · Jan 24, 2015

Then what's sin(a+b)?

Fightfish · Jan 24, 2015

http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html

Math10 · Jan 24, 2015

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