Evaluate $\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 4 ] { x } } d x$
A) Diverges
B) 0
C) $\frac { 4 } { 3 }$
D) $\frac { 3 } { 4 }$

Question

Quizplus · Accepted Answer

The integral $\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 4 ] { x } } d x$ can be rewritten as $\int _ { 1 } ^ { \infty } x^{-\frac{1}{4}} dx$. This is a p-integral with $p = \frac{1}{4}$, which converges if $p > 1$. Since $\frac{1}{4} < 1$, the integral diverges.

Evaluate ∫1∞1x4dx\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 4 ] { x } } d x∫1∞​4x​1​dx

Evaluate $\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 4 ] { x } } d x$