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Math Help - integration

  1. #1
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    integration

    need some help

    if f(x) = x^2
    t^2dt
    x

    then

    f'(x)=
    f'(1)=
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  2. #2
    Eater of Worlds
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    Is that supposed to be f(x)=\int_{x}^{x^{2}}t^{2}dt?.

    If so, \frac{d}{dx}\int_{h(x)}^{g(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)
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  3. #3
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    Prove It's Avatar
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    Quote Originally Posted by dat1611 View Post
    need some help

    if f(x) = x^2
    t^2dt
    x

    then

    f'(x)=
    f'(1)=
    Is this what you're asking?

    If f(x) = \int_x^{x^2}{t^2\,dt}

    what is f'(x) and f'(1)?


    If so... evaluate the integral...

    f(x) = \left[\frac{1}{3}t^3\right]_x^{x^2}

     = \frac{1}{3}(x^2)^3 - \frac{1}{3}x^3

     = \frac{1}{3}x^6 - \frac{1}{3}x^3.


    Now take the derivative...

    f'(x) = 2x^5 - x^2.


    Now let x = 1

    f'(1) = 2\cdot 1^5 - 1^2

     = 1.
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  4. #4
    Math Engineering Student
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    What about if you can't explicitly compute its primitive?
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