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Math Help - [SOLVED] U Substitution Integral

  1. #1
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    Question [SOLVED] U Substitution Integral

    What is the  \int_1^9  \frac{1}{\sqrt{x}} e^{-\sqrt{x}} dx ?

    The answer should be  2e^{-1} - 2e^{-3} .

    How do I use u substitution?

    Thanks for helping!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by juicysharpie View Post
    What is the  \int_1^9 of \frac{1}{\sqrt{x}} e^{-\sqrt{x}} dx ?

    The answer should be  2e^{-1} - 2e^{-3}

    How do I use u substitution?

    Thanks for helping!!
    Let u = - \sqrt{x}

    this would mean du = - \frac 1{\sqrt{x}}~dx, or in other words, -du = \frac 1{\sqrt x}~dx

    can you finish?
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  3. #3
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    Quote Originally Posted by juicysharpie View Post
    What is the integral from 1 to 9 of  (\frac{1}{\sqrt{x}}) (e^-\sqrt{x}) (dx) ?

    The answer should be  2e^{-1} - 2e^{-3}

    How do I use u substitution?

    Thanks for helping!!
    u = -\sqrt{x}

    du = -\frac{1}{2\sqrt{x}} \, dx

    \int_1^9 \frac{1}{\sqrt{x}} \cdot e^{-\sqrt{x}} \, dx

    -2 \int_1^9 -\frac{1}{2\sqrt{x}} \cdot e^{-\sqrt{x}} \, dx

    -2 \int_{-1}^{-3} e^u \, du

    2 \int_{-3}^{-1} e^u \, du

    2(e^{-1} - e^{-3})
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