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Math Help - derivative of a definite integral

  1. #1
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    derivative of a definite integral

    derivative of a definite integral-screen-shot-2012-12-12-12.06.52-am.png

    is this done by cos(e^3)-cos(e^1)
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  2. #2
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    Re: derivative of a definite integral

    \int_1^3\cos(e^y)\,dy is a constant; it does not depend on x. Therefore, its derivative with respect to x is zero.
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    Re: derivative of a definite integral

    The answer emakarov gave is correct, but I'll bet you copied the question incorrectly. Either that or you got a trick question. Did you perhaps mean \frac{d}{dx}\int_1^x\cos{e^y}dy? By the Fundamental Theorem of Calculus, it is equal to \cos{e^x}.

    - Hollywood
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  4. #4
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    Re: derivative of a definite integral

    it was a trick question, thanks!

    what if it were defined on from 2 to x would we still have cos e^x as the derivative of the integral?

    MH
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  5. #5
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    Re: derivative of a definite integral

    Quote Originally Posted by kingsolomonsgrave View Post
    what if it were defined on from 2 to x would we still have cos e^x as the derivative of the integral?
    Yes.
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