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.

Thanks in advace!

  • 1
    $\begingroup$ 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. $\endgroup$ – Stephen Montgomery-Smith Mar 6 '15 at 20:26

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