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Math Help - Derivative of definite integral?

  1. #1
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    Derivative of definite integral?

    Is it possible to take the derivative of a definite integral? I guess if we have an indefinite one, like:
    \int f(x)\,dx, taking its derivative, we would get f(x), right?

    What if we had \int_a^b f(x)\,dx?
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  2. #2
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    wouldn't it be 0? because the solution to the indefinite integral would be a constant, derivative of a constant = 0.
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  3. #3
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    Yes, that is correct. \int_a^b f(x) dx is a constant and its derivative is 0.
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    Thanks guys.

    seld, you meant definite integral right? (not indefinite).
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    Quote Originally Posted by scorpion007 View Post
    Thanks guys.

    seld, you meant definite integral right? (not indefinite).
    Yes, because indefinte integrals can be written as a function of x provided that one of the limits of integration is constant and the other is some x. But a definite integral is a number, and as hallsofivy said, the derivative of a number is always zero.
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    Quote Originally Posted by scorpion007 View Post
    Thanks guys.

    seld, you meant definite integral right? (not indefinite).
    er . . . yes, wow maybe I should stop posting after explaining analysis for about 2 hours to people . . . yes that's a typo thingy
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  7. #7
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    Quote Originally Posted by scorpion007 View Post
    Is it possible to take the derivative of a definite integral? I guess if we have an indefinite one, like:
    \int f(x)\,dx, taking its derivative, we would get f(x), right?

    What if we had \int_a^b f(x)\,dx?
    \int_a^b f(x)\,dx is a definite integral.
    A definite integral is a number. What is the derivative of a number?
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