Determine whether the improper integral converges or diverges, and if it converges, find its value. $\int_{3 \pi}^{\infty} \cos x d x$
A) 6
B) 0
C) 3
D) Diverges

Question

Quizplus · Accepted Answer

The integral of $\cos x$ is bounded between $-1$ and $1$, and the integral does not converge as $x$ approaches infinity since $\cos x$ oscillates indefinitely. Therefore, this improper integral diverges.

Determine Whether the Improper Integral Converges or Diverges, and If ∫3π∞cos⁡xdx\int_{3 \pi}^{\infty} \cos x d x∫3π∞​cosxdx

Determine Whether the Improper Integral Converges or Diverges, and If $\int_{3 \pi}^{\infty} \cos x d x$