# Thread: Integral containing two separate sin functions

1. ## Integral containing two separate sin functions

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?

2. Originally Posted by blorpinbloo
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:

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

3. Originally Posted by blorpinbloo
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 $\displaystyle x$?

4. 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.