Question

Integral Question

Answer 1

\[\int\limits_{0}^{4} \frac{ dx }{ (x-2)^{2/3} }\]

Answer 2

You ARE going to have to cut it up at x = 2 and consider convergence on both sides.

Answer 3

Split it and take limit approaching 2 from left and right?

Answer 4

\[\int_0^4\frac{dx}{(x-2)^{\frac{2}{3}}}=\int_0^2\frac{dx}{(x-2)^{\frac{2}{3}}}+\int_2^4\frac{dx}{(x-2)^{\frac{2}{3}}}\]
The integrand is undefined at x = 2, so you'll have to split up the integrals and take limits.

Answer 5

How do I take the integral of [1/(x-2)]^(2/3)

Answer 6

Simple exponent.

\(\int [1/(x-2)]^{2/3}\;dx = \int [x-2]^{-2/3}\;dx = \dfrac{(x-2)^{1/3}}{1/3} + C\)

Answer 7

Gah... How did I miss that. Thanks.