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Math Help - Finding a Derivative from an Integral

  1. #1
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    Finding a Derivative from an Integral

    Third question of the day...

    p(x)=INTGRL(a=1, b=SQRROOTx) sin^5T. find DY/DY

    Normally, I know how to do this problem, but I don't know when a is 1. I've only done them when a is equal to zero
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Super Mallow View Post
    Third question of the day...

    p(x)=INTGRL(a=1, b=SQRROOTx) sin^5T. find DY/DY

    Normally, I know how to do this problem, but I don't know when a is 1. I've only done them when a is equal to zero
    Do you mean
    p(x) = \int_1^{\sqrt{x}}~sin^5(t)~dt

    and to find \frac{dp}{dx}?

    -Dan
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    Yes, that's exactly it
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Super Mallow View Post
    Yes, that's exactly it
    Use the second fundamental theorem with the chain rule:

    \frac d{dx} \int_a^{g(x)}f(t)~dt = f(g(x)) \cdot g'(x)
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