# Math Help - Integral Proofs

1. ## Integral Proofs

Prove the formula, where m and n are positive integers

a) Integral(-pi to pi) sin(mx) cos(nx)dx = 0.

b) Integral(-pi to pi) sin(mx)sin(nx)dx = 0 if m != n

Integral(-pi to pi) sin(mx)sin(nx)dx = pi if m = n

c) Integral(-pi to pi) cos(mx) cos(nx) dx = 0 if m != n

Integral(-pi to pi) cos(mx) cos(nx) dx = pi if m = n

2. Originally Posted by TreeMoney
Prove the formula, where m and n are positive integers

a) Integral(-pi to pi) sin(mx) cos(nx)dx = 0.

b) Integral(-pi to pi) sin(mx)sin(nx)dx = 0 if m != n

Integral(-pi to pi) sin(mx)sin(nx)dx = pi if m = n

c) Integral(-pi to pi) cos(mx) cos(nx) dx = 0 if m != n

Integral(-pi to pi) cos(mx) cos(nx) dx = pi if m = n

I give you a killer hint.
Use identities

sin x sin y= (1/2)[cos(x-y)-cos(x+y)]

cos x cos y=(1/2)[cos(x-y)+cos(x+y)]

sin x cos y=(1/2)[sin(x+y)+sin(x-y)]

Just curious are you learning Fourier Series?

3. no, this is all different ways of integration. But my issue is I don't remember any trig whats so ever, So I'm trying to learn new material and re-teach basically teach myself all of trig over again. I think the last time I did anything using this much trig was like 6 or 7 years ago.

4. Originally Posted by TreeMoney
no, this is all different ways of integration. But my issue is I don't remember any trig whats so ever, So I'm trying to learn new material and re-teach basically teach myself all of trig over again. I think the last time I did anything using this much trig was like 6 or 7 years ago.
The important thing is to understand how these formulas are true. Then you do not need to memorize them. For example, when you asked this question I did not have to look them up nor memorize these identities. I just know that cos(x+y) leaves cosine with cosine and sine with sine and the rest was trivial. I was just reading CaptainBlank said he does not know the quotient rule but still solved the problem because he understands how it works.