# Integral containing two separate sin functions

• Jun 24th 2010, 01:40 PM
blorpinbloo
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?
• Jun 24th 2010, 03:13 PM
Also sprach Zarathustra
Quote:

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:

$sin(a)sin(b)=\frac{1}{2}[cos(a-b)-cos(a+b)]$
• Jun 24th 2010, 03:55 PM
Prove It
Quote:

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 $y$ and/or $z$ are functions of $x$ or if they are independent of $x$?
• Jun 24th 2010, 04:54 PM
slider142
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.