Question

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Answer 1

\[\int\limits_{0}^{1}x ^{-1/3}dx=\frac{ 3 }{ 2 }x^{2/3} from 1 \to 0 = \frac{ 3 }{ 2 }-0=\frac{ 3 }{ 2 }\] Thus the integral coverges.