Thread: 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?

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.

Originally Posted by Fuji

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 , they mean "evaluate the indefinite integral ".