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Math Help - I need help with integration problem!

  1. #1
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    I need help with integration problem!

    f(x) = integral from 0 to g(x) of ((t+1)/(t^5+1)^.5)dt where g(x) = integral from 0 to sinx of (1+cos(t^3))dt find f'(pi) help please!
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  2. #2
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    Re: I need help with integration problem!

    Quote Originally Posted by kyliealana View Post
    f(x) = integral from 0 to g(x) of ((t+1)/(t^5+1)^.5)dt where g(x) = integral from 0 to sinx of (1+cos(t^3))dt find f'(pi) help please!
    Is the question f(x) = \int_0^{g(x)} {\frac{{t + 1}}{{\sqrt {{t^5} + 1} }}dt} where g(x) = \int_0^{\sin (x)} {\left( {1 + \cos ({t^3})} \right)dt} , find f'(\pi)~?

    If that is it, then the good news is that no integrals are needed.

    f'(x) = \frac{{g(x) + 1}}{{\sqrt {{g^5}(x) + 1} }}g'(x) where g'(x) = \left( {1 + \cos \left( {{{\sin }^3}(x)} \right)} \right)\left( {\cos (x)} \right).

    Now just evaluate that for x=\pi~.
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  3. #3
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    Re: I need help with integration problem!

    Thank you! I have a question though. Why is f'(x) the same as the integral when g'(x) is not the same as the integral?
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  4. #4
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    Re: I need help with integration problem!

    Quote Originally Posted by kyliealana View Post
    Why is f'(x) the same as the integral when g'(x) is not the same as the integral?
    I simply have no idea what your question means. Here is the basic idea.

    If each of h(x)~\&~g(x) is a differentiable function and f(x) = \int_{g(x)}^{h(x)} {\phi (t)dt} then f'(x) = \phi \left( {h(x)} \right)h'(x) - \phi \left( {g(x)} \right)g'(x).
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