How do I integrate sin(120pi*t)cos(120pi*n*t) easily?

[luckyduck]

Homework Statement

How do I integrate this easily?

$\frac{2}{T}$$\int^{T/2}_{0}sin(120\pi t)cos(120\pi n t)$

Homework Equations

The Attempt at a Solution

I used Wolfram Alpha to integrate this, but are there ways to use substitution or another trick instead?

 

[micromass]

Product to sum formulas.

 

[Simon Bridge]

Sure there is!

You start out by understanding the shape of the curve and what it means to integrate it.
Remember that you are finding the area between the curve and the t-axis.
Also, what is the significance of that T/2: does the capital T have a special meaning in context of the operand?
What difference does the 120pi in the trig function make to the shape of the function?
What difference does the n make in the cosine.
Do you know how trig functions combine?
[edit: i.e. the product-to-sum formulas micromass mentions
- when you see combinations of trig functions, it is often useful to arm yourself with a table of identities.]

When you understand what you are doing - things come more easily.

However - just looking at it in terms of a brute force approach: have you tried integration by parts?