Evaluate the integral using integration by parts with the indicated choices of $u$ and $d v$. $\int 6 \theta \cos \theta d \theta , u = 6 \theta , d v = \cos \theta d \theta$
A) $6 \sin \theta + 6 \cos \theta + C$
B) $6 \theta \cos \theta + 6 \sin \theta + C$
C) $6 \theta \sin \theta + 6 \cos \theta + C$
D) $6 \sin \theta - 6 \cos \theta + C$
E) None of these

Question

Quizplus · Accepted Answer

Using integration by parts, we have:
\begin{align*}
\int 6 	heta \cos 	heta d 	heta &= 6 	heta \int \cos 	heta d 	heta - 6\int \sin 	heta d 	heta\
&= 6 	heta \sin 	heta - 6 \cos 	heta + C
\end{align*}
Therefore, the correct choice is (C).

Evaluate the Integral Using Integration by Parts with the Indicated uuu

Evaluate the Integral Using Integration by Parts with the Indicated $u$