Consider the following.

$20$

t$2$ sin$(2$t$)$ dt

This integral can be evaluated using integration by parts with the following choice of u$.$

u $=$ t$2$

Determine dv$,$ du$,$ and v$.$

dv

$=$

sin$(2$t$)$ dt

du

$=$

$2$t dt

v$=$

$12$cos$(2$t$)$

Evaluate the integral.