Determine whether the improper integral converges or diverges.
-$$\int _ { 10 } ^ { \infty } \frac { d x } { \sqrt [ 6 ] { x - 9 } }$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

The integral diverges because the integrand behaves like $ \frac{1}{x^{1/6}} $ as $ x \to \infty $, and the integral of $ \frac{1}{x^{1/6}} $ diverges for $ p \leq 1 $ in the $ \int_{a}^{\infty} \frac{1}{x^p} \, dx $ form.

Determine Whether the Improper Integral Converges or Diverges ∫10∞dxx−96\int _ { 10 } ^ { \infty } \frac { d x } { \sqrt [ 6 ] { x - 9 } }∫10∞​6x−9​dx​

Determine Whether the Improper Integral Converges or Diverges $\int _ { 10 } ^ { \infty } \frac { d x } { \sqrt [ 6 ] { x - 9 } }$