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Math Help - Integral practice

  1. #1
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    Integral practice

    Given:
    \int _1^{x}f(t)dt = x^2 - 2x +1

    Find f(x)
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  2. #2
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    Quote Originally Posted by penguinpwn View Post
    Given:
    \int _1^{x}f(t)dt = x^2 - 2x +1

    Find f(x)
    ... take the derivative of both sides of the equation w/r to x
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  3. #3
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    So would that lead to


    \int _1^{x}f(t)dt = x^2 - 2x +1


    \frac {dt} {dx} = (2x - 2)dx


    Then what?
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  4. #4
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    Quote Originally Posted by penguinpwn View Post
    So would that lead to


    \int _1^{x}f(t)dt = x^2 - 2x +1


    \frac {dt} {dx} = (2x - 2)dx


    Then what?
    are you not familiar with the Fundamental Theorem of Calculus? ...

    \frac{d}{dx} \int_a^x f(t) \, dt = f(x)
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  5. #5
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    I'm relatively new to the subject, but yes.

    I just don't understand how it's applied here
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  6. #6
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    \frac{d}{dx} \left(\int _1^{x}f(t) \, dt = x^2 - 2x +1\right)

    f(x) = 2x-2

    that's all there is to it.
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