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Thread: figuring out a rule..

  1. #1
    Sep 2009

    figuring out a rule..

    ∫1/(x^(3/2)) = -2/sqrt(x) ???

    im trying to figure out the rule here. its poping up a few times. these 2 questions especially:


    (click on "show steps" and look at step 3)

    or here


    (sort of the same question really).

    whats going on there? can someone show the working out to me for how we end up with the answer?
    Last edited by mr fantastic; Sep 28th 2009 at 10:37 PM. Reason: Added url tags.
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  2. #2
    Flow Master
    mr fantastic's Avatar
    Dec 2007
    Quote Originally Posted by Prodigga View Post
    ∫1/(x^(3/2)) = -2/sqrt(x) ???

    You're expected to know the rule $\displaystyle \int x^n \, dx = \frac{1}{n+1} x^{n+1} + C$ where $\displaystyle n \neq -1$. In the above integral $\displaystyle n = - \frac{3}{2}$.

    (You are also expected to be fluent enough with basic index laws to know that $\displaystyle x^{-1/2} = \frac{1}{x^{1/2}} = \frac{1}{\sqrt{x}}$).
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