Integral containing two separate sin functions

Jan 2010
11
0
Hey all, my integration is a bit rusty so I'm having trouble with integrating a function thats something like:

sin(yx)sin(zx)dx

How would I go about a problem like that?
 
Dec 2009
1,506
434
Russia
Hey all, my integration is a bit rusty so I'm having trouble with integrating a function thats something like:

sin(yx)sin(zx)dx

How would I go about a problem like that?
Use the following trigonometric identity:

\(\displaystyle sin(a)sin(b)=\frac{1}{2}[cos(a-b)-cos(a+b)]\)
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
Hey all, my integration is a bit rusty so I'm having trouble with integrating a function thats something like:

sin(yx)sin(zx)dx

How would I go about a problem like that?
It needs to be asked if \(\displaystyle y\) and/or \(\displaystyle z\) are functions of \(\displaystyle x\) or if they are independent of \(\displaystyle x\)?
 
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Reactions: AllanCuz
May 2009
72
21
Brooklyn, NY
Assuming y and z are not functions of x, the integral is independent of these variables and y and z may be treated as constants. Then integration by parts (applied twice to get a multiple of the original integrand) makes short work of this integral.
Otherwise, you need to know those functions of x.