# Thread: Problem with this Integration

1. ## Problem with this Integration

Hello there!

I need help on solving the following equation.

∫ (π+t) cos (nt) dt + ∫ (π-t) cos (nt) dt

I don't know if its clear but its like this "Integral of [(pi + t) into cos (nt)] dt + integral of [(pi - t) into cos (nt)] dt."

I don't know how to continue after I expand each!!!

Any help is much appreciated.

Thanks,

atwinix

2. Hello, atwinix!

Could you restate the problem?
. . Your writing raises many questions.

I need help on solving the following equation. . . . . Equation?

∫ (π+t) cos (nt) dt + ∫ (π-t) cos (nt) dt

I don't know if it's clear but its like this:
"Integral of [(pi + t) into cos (nt)] dt + integral of [(pi - t) into cos (nt)] dt."

What does "into" mean?

If the problem is: . $\int(\pi + t)(\cos(nt)\,dt + \int(\pi - t)\cos(nt)\,dt$
. . why not make one integral?

. . $\int\bigg[\pi\cos(nt) + t\cos(nt) + \pi\cos(nt) - t\cos(nt)\bigg]\,dt \;=\;2\pi\int\cos(nt)\,dt

$

3. "into" means "multiply by."

The problem is exactly just as you stated, Soroban.

But what do I do if the limits on each part is different. Say from -pi < t < 0 for the first part and 0 < t < pi for the second part!!

This integration has to do with a Fourier Series question, which you can check out below.

4. This has been dealt with in the other thread.

RonL