I've looked at various online integral calculators including Wolfram Alpha and I can't find anything for absolute values when it comes to sine and cosine waves.
For example: If I have $y=|\sin(3x)+\sin(7x)|$, and I want to find the integral of it for $x=0$ to $2$, how would I do that?
Maybe consider what the absolute value function does. How could you approach this?
You know from a fundamental level that integrating can be thought of taking the area of something. How an absolute value affect this operation?
Graphing y and |y| may also give you some insight on what the absolute value operation is doing.
Hint: You probably will need to solve f(x) = 0
$\textbf{Hint:}$ $5$ is halfway between $3$ and $7$ which means we can use the expression
$$|\sin(5x-2x)+\sin(5x+2x)| = |2\sin 5x \cos 2x|$$
by sine angle addition formulas.
