Since Differentiation of a sinusoidal function of a certain angular frequency gives a sinusoidal function of the same frequency, does the statement "Integration of a sinusoidal function of certain frequency gives again a sinusoidal of same frequency" holds true or not?

I am asking this as I recall I have read that the second statement does not hold good but I cannot figure out now why.


1 Answer 1


Yes and no.

If you recall from Calculus, if $g(t) = \frac{d}{dt} f(t)$, then $\int g(t)\ dt = f(t) + C$. So, since the derivative of a sinusoid is a sinusoid of the same frequency, if $g(t)$ sinusoidal, its integral must be a sinusoid of the same frequency, plus a constant.

Whether that "plus a constant" bit is going to make you consider the integral of a sinusoid to not be a sinusoid is up to you. Depending on the problem at hand, that constant term may or may not be a deal breaker for the "sinusoid-ness" of the result.

  • 1
    $\begingroup$ If we interpret "gives again a sinusoidal of same frequency" in a strict sense, yes. It indeed gives "a sinusoidal", plus something else $\endgroup$ Sep 18, 2021 at 10:13
  • $\begingroup$ Thanks, I was just wondering what might be the case that integrating a sinusoid giving a really different function. Yeah, I think so that context may not be treating DC component as a part of general sinusoidal signal. $\endgroup$ Sep 18, 2021 at 14:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.