What is the integral of #sin(x)*sin(10x)#?
Use one of the product to sum formulas. Not many of us use them enough to memorize them, but they are easy enough to get.
We want to change a product of sines. We recall the sine and cosine of a sum or difference.
For this problem we'll need
Subtracting the first equation fron the second gives us:
In this problem
Since cosine is an even function, make it
Now integrate each term by simple substitution.
To change a product of cosines, add the two formulas above.