Question

Improper Integral (Integrals with Infinite Limits)

∫dz/(z-1)^(2/3) from 0 to 2

Answer 1

Given integral is-

$\int_0^2\dfrac{dz}{(z-1)^{\frac{2}{3}}} \\[9pt]=\dfrac{(z-1)^{\frac{1}{3}}}{\frac{1}{3}}|_0^2 \\[9pt]=3(2-1)^{\frac{1}{3}}-3(0-1)^{\frac{1}{3}} \\[9pt]=3(1)-3(-1)^{\frac{1}{3}}\\[9pt]=3(1-(-1)^{\frac{1}{3}})$