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Math Help - Derivative of definate intagral / second derivative? idk.

  1. #1
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    Derivative of definate intagral / second derivative? idk.

    find
    (d/dx) ((2)S(x^2)) ((t^3) – 1) dt i.e. derivative of the intagral from 2 to xsquared of t cubed minus one in relation to t

    then find F^II (second derivavtive of F)

    I know capital F means something different than lower case f, but does it matter in this case? I think this problem is a lot easier than I think it is. Help please?
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  2. #2
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    Quote Originally Posted by ifeustel View Post
    find
    (d/dx) ((2)S(x^2)) ((t^3) – 1) dt i.e. derivative of the intagral from 2 to xsquared of t cubed minus one in relation to t

    then find F^II (second derivavtive of F)

    I know capital F means something different than lower case f, but does it matter in this case? I think this problem is a lot easier than I think it is. Help please?
     f'(x) = \frac{d}{dx} \int_{2}^{x^2} t^3-1 dt

     f'(x) = \frac{d}{dx} [\frac{1}{4}t^4-t]_{2}^{x^2}

     f'(x) = \frac{d}{dx} [\frac{1}{4}(x^2)^4-x^2-\frac{1}{4}(2)^4 + 2]

     f'(x) = \frac{d}{dx} [\frac{1}{4}x^8-x^2- 2]

    Better?

    Usually in such a context, the notation [/tex] F'(x) = f(x) [/tex] and hence  F''(x) = f'(x) , which is what you just worked out above ^. But perhaps they mean they want you to find  f''(x) , in which case you would integrate your answer above again.
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