How to integrate this?

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  • #1
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Homework Statement


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

Homework Equations


The answer is -4.

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?
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement


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

Homework Equations


The answer is -4.

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.
 
  • #3
954
117
Er...doesn't the final step that you list give you the answer already?
 
  • #4
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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
LCKurtz
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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##
 
  • #6
954
117
Because sin(x+pi)=sin(x)+sin(pi)
That is most certainly not correct. Can you check your compound angle formula?
 
  • #7
301
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Then what's sin(a+b)?
 
  • #9
301
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@Fightfish , thank you so much for the info! I got it!
 

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