# Math Help - Line Integral Problem

1. ## Line Integral Problem

I have this problem:

Evaluate the line integral, where C is the given curve.
∫C xyz ds
C: x = 9sin(t), y = t, z = -9cos(t), 0 ≤ tπ

After applying the parametrization and everything, I ended up with having to integrate something like: t*sin(t)*cos(t)dt

I have no clue how to integrate that. Integration by parts fails as far as I see, and I can't think of any identities or other tricks to change it to something workable.

2. Originally Posted by Joshai
I have this problem:

Evaluate the line integral, where C is the given curve.
∫C xyz ds
C: x = 9sin(t), y = t, z = -9cos(t), 0 ≤ tπ

After applying the parametrization and everything, I ended up with having to integrate something like: t*sin(t)*cos(t)dt

I have no clue how to integrate that. Integration by parts fails as far as I see, and I can't think of any identities or other tricks to change it to something workable.
Note that $t \sin t \cos t = \frac{1}{2} t \sin (2t)$ via the usual double angle formula. Now use integration by parts.