# Thread: Integral/Cos problems

1. ## Integral/Cos problems

I don't understand why the integral of cos in both pictures is equal to 0. Also in the second picture both cos suffered a transformation in the second step(t1 became t1+t2 etc...).
Could someone explain why this happens? I'm trying to understand but without success.

2. ## Re: Integral/Cos problems

The integral of any sinusoid over an integer multiple of a full period will be zero.

Think about it, you have two identical portions of opposite signs.
Integration results in adding these portions which cancel each other out.

I can't make heads or tails of the second picture but you can do whatever you like to the argument
and as long as you integrate over a integer number of periods the result will be zero.

3. ## Re: Integral/Cos problems

Ok thanks, I understand it more or less now but that integral of a cos with (t1-t2) as argument in the second picture shouldn't be 0 aswell? That is confusing me a bit.

4. ## Re: Integral/Cos problems

Originally Posted by kym
Ok thanks, I understand it more or less now but that integral of a cos with (t1-t2) as argument in the second picture shouldn't be 0 aswell? That is confusing me a bit.
Ok I looked more carefully at this.

The answer is no because the 2nd term is independent of $\theta$

So integrating over $0$ to $2\pi$ just ends up multiplying the integrand by $2\pi$