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## anonymous 3 years ago Integral Question

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1. anonymous

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

2. tkhunny

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. tkhunny

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

7. anonymous

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

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