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Math Help - general form

  1. #1
    Faz
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    Write the general form of the antiderivative of f(x)=4x-2x^2+x*Sqrt(x) + e^x.

    Hence calculate integral of 0 to 1 for the above equation
    Last edited by mr fantastic; December 15th 2008 at 02:40 AM.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by Faz View Post
    write the general form of the antiderivative of f(x)=4x-2x^2+x*Sqrt(x) + e^x
    Note that \sqrt{x}=x^{1/2}
    Hence x*\sqrt{x}=x^{3/2}

    Now here are a few points to help you find the antiderivative :
    - an antiderivative for x^n is \frac{x^{n+1}}{n+1}
    - an antiderivative of a sum is the sum of the antiderivatives
    - an antiderivative of e^x is e^x
    - don't forget the integration constant.

    hence calculate integral of 0 to 1 for the above equation
    Let F be the antiderivative you've found.

    The integral from 0 to 1 is defined as follows :
    \int_0^1 f(x) ~ dx=F(1)-F(0)
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