Determine whether the improper integral converges or diverges, and if it converges, find its value. $$\int _ { - 27 } ^ { 8 } \frac { 1 } { \sqrt [ 3 ] { x } } d x$$
A) 15
B) $- \frac { 15 } { 2 }$
C) Diverges
D) $\frac { 15 } { 2 }$

Question

Quizplus · Accepted Answer

The integral converges and evaluates to $- \frac { 15 } { 2 }$. The function $\frac{1}{\sqrt[3]{x}}$ is integrable over $[-27, 8]$ since it is continuous on this interval, and the antiderivative can be found and evaluated at the bounds.

Determine Whether the Improper Integral Converges or Diverges, and If ∫−2781x3dx\int _ { - 27 } ^ { 8 } \frac { 1 } { \sqrt [ 3 ] { x } } d x∫−278​3x​1​dx

Determine Whether the Improper Integral Converges or Diverges, and If $\int _ { - 27 } ^ { 8 } \frac { 1 } { \sqrt [ 3 ] { x } } d x$