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Math Help - complicated integral

  1. #1
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    complicated integral

    Consider the function.



    Find F''(2)


    (thanks in advance..
    [IMG]file:///C:/Users/rsanford/AppData/Local/Temp/moz-screenshot.jpg[/IMG][IMG]file:///C:/Users/rsanford/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rsanford View Post
    Consider the function.



    Find F''(2)


    (thanks in advance..
    [IMG]file:///C:/Users/rsanford/AppData/Local/Temp/moz-screenshot.jpg[/IMG][IMG]file:///C:/Users/rsanford/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]
    these are just using the second fundamental theorem of calculus: in a nutshell it says:

    if f(x) = \int_c^{g(x)}f(t)~dt, then f'(x) = f(g(x)) \cdot g'(x)

    where c is any constant and g(x) is some function of x.

    Use this to find f'(x). then to get f''(x), just take the regular derivative of f'(x)

    Can you continue?
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  3. #3
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    yes! Thank you! I just didn't see that.
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  4. #4
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    I'm sorry.. I'm having trouble taking the integral of
    <br /> <br />
\int_1^{x^2} \frac{\sqrt{5+x^4}}{x}<br /> <br />
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by rsanford View Post
    I'm sorry.. I'm having trouble taking the integral of
    <br /> <br />
\int_1^{x^2} \frac{\sqrt{5+x^4}}{x}<br /> <br />
    Make a trig substitution with 5\tan(\theta)
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rsanford View Post
    I'm sorry.. I'm having trouble taking the integral of
    <br /> <br />
\int_1^{x^2} \frac{\sqrt{5+x^4}}{x}<br /> <br />
    the point of my first post was showing that you do not have to do any integrals here. just use the fundamental theorem of calculus that i posted. do you understand what the theorem says? all you need for this problem is derivatives, and that's only because we are going to the second derivative. DO NOT EVALUATE ANY INTEGRALS.

    Quote Originally Posted by Mathstud28 View Post
    Make a trig substitution with 5\tan(\theta)
    that would not work...
    Last edited by ThePerfectHacker; April 22nd 2008 at 07:18 PM.
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  7. #7
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Jhevon View Post
    that would not work...
    I havent worked it but letting x^2=5tan(\theta)?

    o wait I see why..hmm...well then that makes that harder
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    I havent worked it but letting x^2=5tan(\theta)?

    o wait I see why..hmm...well then that makes that harder
    yes, the fourth power is the problem. thank God we don't have to do this integral
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