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Math Help - Is there a chain rule for intergration?

  1. #1
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    Is there a chain rule for intergration?

    What would be the rule for something like this?

    \[\int_4^6 \left(\frac{d}{dt}\sqrt{4 + 4 t^4}\right)\, dt\]
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  2. #2
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    You can take the derivative of \sqrt{4 + 4 t^4} and integrate the result?
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  3. #3
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    \displaystyle \int_a^bf'(x) dx = f(b)-f(a).
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  4. #4
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    wait..I got it. At least I think I got it.

    \sqrt{4}\int_{4}^{6}\frac{1}{(1+0)}t^{1+0}+\sqrt{4  }\int_{4}^{6}\frac{1}{(1+4)}t^{4+1}

    Nevermind I got it from the above post.
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  5. #5
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    Quote Originally Posted by TheCoffeeMachine View Post
    \displaystyle \int_a^bf'(x) dx = f(b)-f(a).
    To make it crystal clear for the OP, I'd state it as \displaystyle \int_a^b \frac{df}{dx} \, dx = f(b)-f(a).
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  6. #6
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    \int_{ 2 } ^ { 7 } (2 x + 8) dx

    I think something like this is what I take the anti-derivative of.

    Yeah I got it now, I just now have to deal with a long tedious task of entering in the answers.

    This is a lot easier than reimann sums
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  7. #7
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    The "chain rule for integration" (i.e. the inverse of the chain rule) is "substitution".
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