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Thread: another improper integral problem

  1. #1
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    another improper integral problem

    $\displaystyle \int \frac{4}{x^\frac{4}{3}}dx$ [1,infinity]

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

    Did I work this out right correctly so far? If so, I'm not sure how to solve it...
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  2. #2
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    $\displaystyle \lim_{b \to \infty} \int_1^{\infty} 4x^{-\frac{4}{3}} \, dx$

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

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