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Math Help - What are the the difference among integral, antiderrivative, derivate and a function?

  1. #1
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    What are the the difference among integral, antiderrivative, derivate and a function?

    I am trying to understand the difference among integral, antiderrivative, derivate and a function. I understand that a function is just a function (ex: x^2) which has a derivative of 2x. But what is the main difference between antiderrivative and integral? Do I get integral if I flip the graph of a derivative or a function? Can anyone explain please?
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  2. #2
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    Let's say...

    Your function = X^2
    Your Derivative will = 2X
    Your Anti Derivative will = 1/3*X^3

    An anti derivative is basically, "What function did I have before to get this derivative -- in this case, x^2?"

    I don't think there is a huge difference between an integral and anti derivative because if I say, "I'm integrating this function." or "I'm taking the anti derivative of this function." They mean the same thing.

    Integrals and anti derivatives share this sign:

    Spoiler:




    If you get...

    "The integral from x=1 to x=4 on the graph x^2," then that means you're finding the AREA UNDER THE CURVE X^2 between x=1 and x=4. It's not as simple as flipping a derivative. For this kind of problem, you'll need to take the anti derivative of x^2 and continue on with the Second Fundamental Theorem of Calculus.

    Someone else can probably explain it better than me.
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  3. #3
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    Quote Originally Posted by Fuji View Post
    I don't think there is a huge difference between an integral and anti derivative because if I say, "I'm integrating this function." or "I'm taking the anti derivative of this function." They mean the same thing.
    Usually, when someone asks you to take the anti-derivative of a function f(x), they mean "evaluate the indefinite integral \int f(x) dx".
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