How to solve this triple integral?

  • Thread starter Nah_Roots
  • Start date
  • #1
6
0
\int \int \int cos(u + v + w)dudvdw (all integrals go from 0 to pi).

I've tried using u substitution for each integral but I end up with a huge integral.
 
Last edited:

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
965
I don't see why. To integrate cos(u+v+w)du, let x= u+ v+ w so dx= du. The integral becomes [itex]\int[/itex] cos(x)dx= -sin(x)+ C= -sin(u+ v+ w)+ C. Evaluating that at 0 and pi gives -sin(pi+ v+ w)+ sin(v+ w). But sin(x+ pi)= -sin(x) so that is just 2 sin(v+w).

Now integrate 2sin(v+w) dv by letting x= v+ w so dx=dv.
 
  • #3
6
0
I don't understand sin(x+ pi)= -sin(x). Is that an identity I am forgetting about?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,847
965
Do you know what the graph of y= sin(x) looks like?
 
  • #5
6
0
Oh, I see. It's a shift, correct?
 

Related Threads on How to solve this triple integral?

  • Last Post
Replies
12
Views
291
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
9
Views
824
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
986
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
1K
Top