another improper integral problem

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• March 7th 2009, 06:06 AM
saiyanmx89
another improper integral problem
$\int \frac{4}{x^\frac{4}{3}}dx$ [1,infinity]

$lim (\frac{-12}{x^{\frac{1}{3}}})| [1,b]$
$b->infinity$

Did I work this out right correctly so far? If so, I'm not sure how to solve it...
• March 7th 2009, 06:24 AM
skeeter
$\lim_{b \to \infty} \int_1^{\infty} 4x^{-\frac{4}{3}} \, dx$

$\lim_{b \to \infty} \left[-12x^{-\frac{1}{3}}\right]_1^b$

$-12 \lim_{b \to \infty} \left[b^{-\frac{1}{3}} - 1^{-\frac{1}{3}}\right] = -12(0 - 1) = 12
$