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Thread: Integral Problem

  1. #1
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    Integral Problem

    In this problem $\displaystyle F(1)$ where $\displaystyle F'(x)=e^{-t^2}$

    And$\displaystyle F(0) = 2$

    find the value of the function so I wind up with this

    $\displaystyle F(x) = 2 + \int e^{-t^2}$

    plug in one for x but how do I anti differentiate this

    $\displaystyle \int e^{-t^2}$
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  2. #2
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    Hello The Power!

    Quote Originally Posted by The Power View Post
    In this problem $\displaystyle F(1)$ where $\displaystyle F'(x)=e^{-t^2}$
    Huh? Is it $\displaystyle F'(t) = e^{-t^2}$ ? Because I think it should be


    Quote Originally Posted by The Power View Post
    And$\displaystyle F(0) = 2$

    find the value of the function so I wind up with this

    $\displaystyle F(x) = 2 + \int e^{-t^2}$
    It would be better, if you first calculate

    $\displaystyle F'(t) = e^{-t^2}$

    => $\displaystyle F(t) = \int e^{-t^2} dt + c$

    and then you substitute t = 0, so you solve F(0) = 2 to solve for c.


    Quote Originally Posted by The Power View Post
    plug in one for x but how do I anti differentiate this

    $\displaystyle \int e^{-t^2}$
    Do you know integration by substitution?

    Use the substitution z = t^2... That would work.



    Yours
    Rapha
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  3. #3
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    Thanks Rapha!
    Im currently learning how to do substitution is it quite tricky because at first I made u = -t^2 and do i not know when to solve for du = some derivative dx completely for dx if you can make any sense of that

    In this case C = 2 so its

    2 + integral

    If this is correct
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  4. #4
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    Quote Originally Posted by The Power View Post
    In this problem $\displaystyle F(1)$ where $\displaystyle F'(x)=e^{-t^2}$

    And$\displaystyle F(0) = 2$

    find the value of the function so I wind up with this

    $\displaystyle F(x) = 2 + \int e^{-t^2}$

    plug in one for x but how do I anti differentiate this

    $\displaystyle \int e^{-t^2}$
    $\displaystyle \int{e^{-t^2}\,dt}$ does not have a solution from elementary functions.
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  5. #5
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    So how do I obtain a value for F(1) somehow the book retrieved the answer numerically of 2.747
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  6. #6
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    Quote Originally Posted by The Power View Post
    So how do I obtain a value for F(1) somehow the book retrieved the answer numerically of 2.747
    As said earlier, a closed form solution using elementary functions cannot be obtained. The book would have used technology to get an approximate value.
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  7. #7
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    I wish the book would state this but sadly they do not I should just skip through those type of problems because calculators are not allowed on test
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