Why Is My Integral Result Incorrect for Cosine of 2 Theta?

[PieOperator]

Homework Statement

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

Homework Equations

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?

 

[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-θ1^π+θ₁ …

what happened then? ​

 

[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.