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Thread: "Integration", opposite of "Derivation"?

  1. #1
    Newbie petike's Avatar
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    Question "Integration", opposite of "Derivation"?

    Hi,
    I am new to integration (or integral) and something is not clear to me.
    At school they taught me that integral can express "the area under the curve" (of graph). That's clear to me.
    But they also taught me that integral is the opposite of derivative. And here's the problem.
    Can I understand it that if I differentiate some function and then integrate the new function, I'll get the original one?

    For example, let's differentiate this function:

    f(x) = 3x^4 + 2
    f'(x) = 12x^3

    So the integral of function:

    \int12x^3 =? \ 3x^4 + 2 \ \ \ ???


    Thanks.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    differentiate these functions ...

    f(x) = 3x^4 + 95

    f(x) = 3x^4 - 1

    f(x) = 3x^4 + \pi

    f(x) = 3x^4 + 12.6

    f(x) = 3x^4 - 10^{100}

    so ... what does that tell you about \int 12x^3 \, dx ???
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