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Math Help - Integral problem w/ both limits as variable

  1. #1
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    Integral problem w/ both limits as variable

    Hey all, I'm very new to these forums. I'm not looking for the answers, but rather to figure out if the way I go about doing this problem is correct or if I am totally wrong any explanation would be very appreciated.

    Question: Use the fundamental theorem of Calculus to find the derivative of the given function
    \int_{x^3}^{x} cos(t^3)dt

    What I did:
    \int_{x^3}^{x} cos(t^3)dt = \int_{0}^{x} cos(t^3)dt - \int_{0}^{x^3} cost(t^3)dt =  cos(x^3) - cos(x^9) * 3x^2

    **Ive never used LaTeX before so I hope this is the right way of showing it.
    **If I messed up the whole thing or any part please give me tips on where I went wrong, thank you!

    P.S - is there any online program that I could input an integral such as this so I can check myself?

    Sorry for all the questions + thank you!
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  2. #2
    MHF Contributor
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    Looks good. Latex good too! Tiny typo cost(t...

    I don't think that http://www.wolframalpha.com/ can do this particular task, at least, my attempt to input

    differentiate int _(x^3) ^x cos(t^3) dt

    caused 'server unavailable' - my syntax possibly wrong...
    Last edited by tom@ballooncalculus; February 15th 2010 at 12:59 PM. Reason: no edit after all
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  3. #3
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    Thanks for your help . Ive also tried using that web-site but it does not seem to work for me either >.<;;
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  4. #4
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    nevermind...i just noticed you have it right...didnt even check till after i posted...lol...time to take a break. later on.
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