Evaluate the integral using integration by parts with the indicated choices of u and dv. $$\int 6 \theta \cos \theta d \theta , u = 6 \theta , d v = \cos \theta d \theta$$
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 with $u = 6	heta$ and $dv = \cos	heta~d	heta$, we have $du = 6~d	heta$ and $v = \sin 	heta$. Thus, we have:

$$\int 6 	heta \cos 	heta d 	heta = 6 	heta \sin 	heta - \int 6\sin 	heta d	heta$$

Simplifying, we get:

$$\int 6 	heta \cos 	heta d 	heta = 6 	heta \sin 	heta + 6\cos 	heta + C$$

Therefore, the answer is (C).

Evaluate the Integral Using Integration by Parts with the Indicated ∫6θcos⁡θdθ,u=6θ,dv=cos⁡θdθ\int 6 \theta \cos \theta d \theta , u = 6 \theta , d v = \cos \theta d \theta∫6θcosθdθ,u=6θ,dv=cosθdθ

Evaluate the Integral Using Integration by Parts with the Indicated $\int 6 \theta \cos \theta d \theta , u = 6 \theta , d v = \cos \theta d \theta$