Evaluate the indefinite integral.

  • Thread starter CellCoree
  • Start date
  • #1
CellCoree
42
0
[tex] \int sin(7x)sin(13x)dx [/tex]

i just need to know how to start this, i can't use u-du...
i can't borrow anything...
so how would i start this?
 

Answers and Replies

  • #2
Tide
Science Advisor
Homework Helper
3,089
0
Is the integrand the same as
[tex]\frac {\cos {6x} - \cos {20x}}{2}[/tex]
?
 
  • #3
teknodude
157
0
One way is to look at the back of your physics or calculus book for a table of indefinite integrals. You should be able to solve it by the equations in the table.
 
  • #4
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
23
As tide is suggesting, one way is to use your trig identities. (Sigh, nobody learns their trig identities these days) The product of two sines, two cosines, or a sine and a cosine can always be converted into a sum of two sines, or a sum of two cosines. The identities can probably be found in your calc or precalc book.

Another approach, if you've learned the necessities, is to replace the sine function with its definition in terms of complex exponentials.

Another way is to use the angle sum identities. Your problem is that 7x and 13x have different coefficients, so break 13x into 7x + 6x and use the sum of angles identity for sine. Rinse, and repeat until you can do all of the resulting integrals. One thing you should always try and find, when dealing with complicated integrals, is an operation that changes a piece of the integral from something you can't handle into something you can.
 
  • #5
ehild
Homework Helper
15,543
1,915
Tide said:
Is the integrand the same as
[tex]\frac {\cos {6x} - \cos {20x}}{2}[/tex]
?

YES!

You know, [tex]cos(\alpha +\beta )= cos(\alpha )cos(\beta ) - sin(\alpha )sin(\beta) \mbox { and } cos(\alpha -\beta )= cos(\alpha )cos(\beta ) + sin(\alpha )sin(\beta)\mbox. \\ [/tex]
[tex]\alpha = 13x \mbox{ and } \beta = 7x [/tex]...

ehild
 

Suggested for: Evaluate the indefinite integral.

Replies
5
Views
321
Replies
5
Views
565
Replies
19
Views
543
Replies
4
Views
236
  • Last Post
Replies
9
Views
448
  • Last Post
Replies
10
Views
366
Replies
5
Views
379
Replies
7
Views
402
Replies
2
Views
1K
Top