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Math Help - integral help! urgent!

  1. #1
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    integral help! urgent!

    integral of (x^(1/2))e^(x^(1/2))

    upper limit = 4
    lower limit = 0

    how do I do this?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by khood View Post
    integral of (x^(1/2))e^(x^(1/2))

    upper limit = 4
    lower limit = 0

    how do I do this?
    I have found that u-substitution is the most useful method of indefinite integration

    \int\sqrt{x}e^{\sqrt{x}}~dx

    Let \sqrt{x}=z\implies x=z^2 so dx=2z~dz so our integral becomes

    \int\sqrt{x}e^{\sqrt{x}}~dx\stackrel{\sqrt{x}=z}{\  longmapsto}2\int ze^{z}\cdot z~dz

    which can be done by parts.
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  3. #3
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    i keep getting the wrong answer when i use that method
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by khood View Post
    i keep getting the wrong answer when i use that method
    Why not try posting some of your computations?
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  5. #5
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    when i use integration by parts I end up with a^2e^2 - 2ae^a + 2e^a
    (all the a's evaluated from 2 to 0) the answer im looking for is 53.598 according to the integral function on my calculator but I don't get anything close to that
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by khood View Post
    when i use integration by parts I end up with a^2e^2 - 2ae^a + 2e^a
    (all the a's evaluated from 2 to 0) the answer im looking for is 53.598 according to the integral function on my calculator but I don't get anything close to that
    \begin{aligned}2\int_0^2 x^2\cdot e^x~dx&=2x^2\cdot e^x\bigg|_{x=0}^{x=2}-4\int_0^2 x\cdot e^x~dx\\<br />
&=8e^2-\left(4x\cdot e^x\bigg|_{x=0}^{x=2}-4\int_0^2 e^x~dx\right)\\<br />
&=8e^2-8e^2+4e^x\bigg|_{x=0}^{x=2}\\<br />
&=4e^2-4\end{aligned}

    Im sure you can fill in the missing steps
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