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Math Help - Improper integral

  1. #1
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    Improper integral

    Integral of 1/(sqrt(1-x)) from 0 to 1.


    I am getting -2*sqrt(1-x) for the integral and then from 0 to 1 it would appear to be 0 - (-2) or 2 to be the answer?

    Please advice.
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  2. #2
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    Quote Originally Posted by WartonMorton View Post
    Integral of 1/(sqrt(1-x)) from 0 to 1.


    I am getting -2*sqrt(1-x) for the integral and then from 0 to 1 it would appear to be 0 - (-2) or 2 to be the answer?

    Please advice.

    \lim_{\epsilon\rightarrow 0}\int\limits^{1-\epsilon}_0\frac{dx}{\sqrt{1-x}}=\lim_{\epsilon\rightarrow 0}\,-2\left[\sqrt{1-x}\right]^{1-\epsilon}_0=  \lim_{\epsilon\rightarrow 0}\,-2(\sqrt{\epsilon}-1)=2

    So you're answer seems to be correct.

    Tonio
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