Evaluate $\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 8 ] { x } } d x$
A) $\frac { 8 } { 7 }$
B) $\frac { 7 } { 8 }$
C) 0
D) Diverges

Question

Quizplus · Accepted Answer

The integral $\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 8 ] { x } } d x$ diverges because the exponent of $x$ in the denominator is less than 1, specifically $x^{-1/8}$, which means the integral diverges as $x$ approaches infinity.

Evaluate ∫1∞1x8dx\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 8 ] { x } } d x∫1∞​8x​1​dx

Evaluate $\int _ { 1 } ^ { \infty } \frac { 1 } { \sqrt [ 8 ] { x } } d x$