# Homework Help: Cosine of 2 times theta

1. Jun 17, 2011

### PieOperator

1. The problem statement, all variables and given/known data

From angles pi minus theta1 to pi plus theta1, what is the integral of cosine of 2 theta times d theta?

2. Relevant equations

3. The attempt at a solution

When I evaluate this definite integral from pi minus theta1 to pi plus theta1, I get positive one half sine of 2 theta1.
It should be NEGATIVE one half sine of 2 theta1.

Is 2pi + 2theta1 and 2pi - 2theta1 somehow wrong????

2. Jun 18, 2011

### tiny-tim

Hi PieOperator!

(have a pi: π and a theta: θ and an integral: ∫ and try using the X2 tag just above the Reply box )

you should have got [1/2 sin2θ]π-θ1π+θ1

what happened then?

3. Jun 18, 2011

### PieOperator

Thanks. I found my mistake. It has to do with vectors and the correct orientation. It is positive one half sine of 2 theta in the incorrect vector orientation. I just have to reverse the direction of the vector, and the interval reverses as well.