# Math Help - Integral of t cos pi t

1. ## Integral of t cos pi t

I am working on a hw problem for multivariable calc that I can't figure out

If r(t)=(t^2)i + (tcospit)j + (sinpit)k
Evaluate integral r(t) from 0 to 1.

I understand that if the vector is composed of 3 component functions, then the integral of the vector is the integrals of the component functions.

So I have (1/3 t^3)i + (integral tcospit)j + (-1/pi cospit)k evaluated from 0 to 1.

I can't figure out integral tcospit. Is there a substituition I am missing or an identity I can use?

Thank

2. Hi

You need to integrate by parts
$\int t\:\cos\left(\pi t\right) dt$

using
$u = t$ and $dv = \cos\left(\pi t\right) dt$