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Math Help - fundamental theorem of calculus help!!!!!!

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    fundamental theorem of calculus help!!!!!!

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    Use the Fundamental theorem of calculus to evaluate the integral ∫ √xdx
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  2. #2
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    Quote Originally Posted by GabrielKiefer View Post
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    Use the Fundamental theorem of calculus to evaluate the integral ∫ √xdx
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    \int_1^4 \sqrt{x} \, dx = \int_1^4 x^{1/2} \, dx.

    And you're expected to know the following:

    1. \int x^n \, dx = \frac{x^{n+1}}{n+1} + C where n \neq -1.

    2. If F(x) = \int f(x) \, dx then \int_a^b f(x) \, dx = F(b) - F(a).
    Last edited by mr fantastic; December 23rd 2008 at 04:21 AM.
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    Quote Originally Posted by GabrielKiefer View Post
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    Use the Fundamental theorem of calculus to evaluate the integral ∫ √xdx
    1
    The fundamental theorem of calculus tell you that:

     <br />
\int_a^b \frac{df}{dx}\ dx=f(b)-f(a)<br />

    and you should also know that:

     <br />
\sqrt{x}=x^{1/2}=\frac{d}{dx}\left(\frac{2}{3}x^{3/2}\right)<br />
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