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Math Help - Definite Integral

  1. #1
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    Definite Integral

    If f(x) = ∫4x^3 (x^3 on top, 4 on bottom) t^5 ,

    find f'(x)

    find f'(4)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by derekjonathon View Post
    If f(x) = ∫4x^3 (x^3 on top, 4 on bottom) t^5 ,

    find f'(x)

    find f'(4)
    You'll need to apply the FTC part 1:

    \frac{\,d}{\,dx}\left[\int_{a}^{g(x)}f\!\left(t\right)\,dt\right]=f\!\left(g\!\left(x\right)\right)\cdot g^{\prime}\!\left(x\right).

    Can you take it from here?
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  3. #3
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    I don't understand....

    How the g(x) relates to the t^5dt part.....

    how do I show a function of x^3 when I don't even see the variable (x) in the part that says t^5dt?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    See attachment
    Attached Thumbnails Attached Thumbnails Definite Integral-2dftc.jpg  
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  5. #5
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    I still can't figure the solution out...

    It seems like it should be simple, but I'm just not getting it. How do I find f'(x)?
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  6. #6
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    Quote Originally Posted by derekjonathon View Post
    It seems like it should be simple, but I'm just not getting it. How do I find f'(x)?
    You will need to post the integral in your question more clearly - it's clear that what we think it is is different to what you think it is.
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