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Thread: [SOLVED] U Substitution Integral

  1. #1
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    Question [SOLVED] U Substitution Integral

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

    The answer should be $\displaystyle 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 $\displaystyle \int_1^9 of \frac{1}{\sqrt{x}} e^{-\sqrt{x}} dx$ ?

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

    How do I use u substitution?

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

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

    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 $\displaystyle (\frac{1}{\sqrt{x}}) (e^-\sqrt{x}) (dx)$ ?

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

    How do I use u substitution?

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

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

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

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

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

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

    $\displaystyle 2(e^{-1} - e^{-3})$
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