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Math Help - help with integral

  1. #1
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    help with integral



    f' (x)=
    f' (1)=

    can anyone solve this?
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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by dat1611 View Post


    f' (x)=
    f' (1)=

    can anyone solve this?
    f\left( x \right) = \int\limits_x^{{x^2}} {{t^2}dt}  = \left. {\frac{{{t^3}}}{3}} \right|_x^{{x^2}} = \frac{{{x^6}}}{3} - \frac{{{x^3}}}{3}.

    f'\left( x \right) = 2{x^5} - {x^2}.

    f'\left( 1 \right) = 2 \cdot 1 - 1 = 1.
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  3. #3
    Math Engineering Student
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    f(x)=\int_{x}^{x^{2}}{t^{2}\,dt}\implies f'(x)=x^{4}\cdot 2x-x^{2}=2x^{5}-x^{2}.
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