Determine whether the improper integral converges or diverges.
-$$\int _ { 1 } ^ { \infty } \frac { | \sin x | } { x ^ { 2 } } d x$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

The integral $\int _ { 1 } ^ { \infty } \frac { | \sin x | } { x ^ { 2 } } d x$ converges because the function $\frac { | \sin x | } { x ^ { 2 } }$ is positive and decreasing for $x \geq 1$, and it is dominated by $\frac{1}{x^2}$, which is a convergent p-series with $p = 2 > 1$.

Determine Whether the Improper Integral Converges or Diverges ∫1∞∣sin⁡x∣x2dx\int _ { 1 } ^ { \infty } \frac { | \sin x | } { x ^ { 2 } } d x∫1∞​x2∣sinx∣​dx

Determine Whether the Improper Integral Converges or Diverges $\int _ { 1 } ^ { \infty } \frac { | \sin x | } { x ^ { 2 } } d x$