Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How is $$\int_0^T\cos(2\omega t+ 2\theta) dt = 0$$ Regards

share|cite|improve this question
What can be said about $w$, $\theta$ and $T$? – AD. Oct 31 '12 at 14:42
up vote 2 down vote accepted

$$\frac{d}{dx}\sin(mx + c) = m cos(mx + c)$$

so backwards we have

$$\int \cos(2wt + 2 \theta) dt = \frac{1}{2w} \sin(2wt + 2 \theta) + c $$

and you can evaluate that at the limits.

share|cite|improve this answer
@PeterPhipps, thanks! – sperners lemma Oct 31 '12 at 15:11

Following Sperners' solution:

$$\int_0^T\cos (2wt+2\theta)\,dt=\left.\frac{1}{2w}\sin (2wt+2\theta)\right|_0^T=\frac{1}{2w}\left[\sin\left(2wT+2\theta\right)-\sin \left(2\theta\right)\right]$$

and the above is zero iff

$$\sin(2wT+2\theta)=\sin 2\theta\Longleftrightarrow 2wT+2\theta=2\theta\,\,\vee\,\,2wT+2\theta=\pi-2\theta$$

So the claim is false unless some relations or given values apply to $\,w,T,\theta\,$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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