# Improper and definitive integral of trigonometric functions involving absolute values

Let $x(t)=10\cos(100t+300°)-5\sin(220t - 50°)$ . It is asked to evaluate the following integrals:

$$\int_{-\infty}^\infty |x(t)|^2 dt \text{ and } \frac{1}{T} \int_{-T}^T |x(t)|^2 dt$$

Where $T$ is the period of this function(which is 18).

I was wondering if is that a easy way to evaluate this whithout calculating the integral of the trigonometric functions. Also, I dont knoe how to do this with this modulus.

• Since $x(t)$ is real, you can just use $|x(t)|^2 = (x(t))^2$, and just multiply it out. Then I think you should just compute the indefinite integrals. There are slicker ways to do it using Parseval's formula, but I suspect this question is trying to lead you to find the formula for yourself. – Stephen Montgomery-Smith Mar 6 '15 at 20:26