Evaluate $\int _ { 1 } ^ { \infty } \frac { d x } { \sqrt [ 3 ] { x } }$ .
A) 0
B) 1
C) $\frac { 1 } { 3 }$
D) Diverges

Question

Quizplus · Accepted Answer

The integral evaluates to an improper integral due to the upper limit of infinity. To solve, we first find the antiderivative of $x^{-\frac{1}{3}}$, which is $3x^{\frac{2}{3}}$, and then evaluate this from 1 to infinity. As the upper limit approaches infinity, the value of $3x^{\frac{2}{3}}$ also approaches infinity, indicating that the integral diverges.

Evaluate ∫1∞dxx3\int _ { 1 } ^ { \infty } \frac { d x } { \sqrt [ 3 ] { x } }∫1∞​3x​dx​

Evaluate $\int _ { 1 } ^ { \infty } \frac { d x } { \sqrt [ 3 ] { x } }$