# Thread: integrals and antiderivative

1. ## integrals and antiderivative

hi, can someone please explain what integrals are? and what exactly is antiderivative also?

I need the basics and if you can please explain to me in a simple way, it would be nice

I have been searching for the meanings and basics of these 2 terms, and all I get are new terms that i dont understand.
I am currently taking Calculus in HS, and I am not doing so well.

So if someone would be so kind and help me, i would appreciate it greatly.

Thank you in advance!

2. Originally Posted by sess
hi, can someone please explain what integrals are? and what exactly is antiderivative also?

I need the basics and if you can please explain to me in a simple way, it would be nice

I have been searching for the meanings and basics of these 2 terms, and all I get are new terms that i dont understand.
I am currently taking Calculus in HS, and I am not doing so well.

So if someone would be so kind and help me, i would appreciate it greatly.

Thank you in advance!
It would be better for you to get a book that explained these things. Calculus for Dummies Amazon.com: Calculus for Dummies: Mark Ryan: Books, The Complete Idiot's Guide To Calculus Amazon.com: The Complete Idiot's Guide to Calculus, 2nd Edition (Complete Idiot's Guide to): W. Michael Kelley: Books may pitch at the level you need. Do you have a textbook?

Alternatively, I'm sure any search engine will turn up gazillions of hits, some will be useful to you.

3. Originally Posted by sess
hi, can someone please explain what integrals are? and what exactly is antiderivative also?

I need the basics and if you can please explain to me in a simple way, it would be nice

I have been searching for the meanings and basics of these 2 terms, and all I get are new terms that i dont understand.
I am currently taking Calculus in HS, and I am not doing so well.

So if someone would be so kind and help me, i would appreciate it greatly.

Thank you in advance!
I can relate to your problem.

Calculus was not taught to us in High School. I encountered Calculus in my college years already, and we were given one semester each only of Differential and Integral Calculus until we graduated. Believe it or not.

So we students who cared had to go to the libraries to supplement whatever was being taught us in the classrooms.

When I joined Math forums later on, .... much, much later on, (eons, if measured by years) .... I was overwhelmed by the popularity of Calculus in the forums. So, just not to feel left out, I searched the web for Calculus. (Here, "overwhelmed" is not relevant anymore because the web will give you Calculus websites by the billions! I mean, if you are not stubborn enough, you better forget Calculus altogether. Imagine how huge is Calculus, it turns out! It got epsilons, limits, vectors, etc... [That said, in most parts, Calc is just Trig in steroids really]).

So what do I understand by antiderivative and integral in the same line of thought or concept?

Antiderivative is the "going back to where the derivative was taken".
While integral is the family of the antiderivative.

Say, a function, f(x) = 3x^2 -5x +4
The first derivative of f(x) is f'(x) = 6x -5

Derivative: 6x -5
What is the antiderivative?
It is 6[(1/2)x^2] -5x
= 3x^2 -5x

Derivative: 6x -5
What is the integral?
INT[6x -5]dx = (6/2)x^2 -5x +C
= 3x^2 -5x +C

You see, neither the antiderivative nor the integral was able to go back to the original 3x^2 -5x +4.

But the integral is the antiderivative if C = 0.
And the integral is the original function if C = 4.

So the integral is a family of the function that the antiderivative is trying to get back to.
The antiderivative is a member of the integral.
The original function is also a member of the integral.
It all depends on what the C of the integral is.

Umm, if you were able to follow, you're okay.
If you were lost evermore, sorry.

4. ## to ticbol

first, i would like to thank you for helping me out, i really apreciate it
second, i understand the concepts now, all thx to u!

however, can you explain how you figured out the antiderivative and the integral? I understand how you do the first derivative, and I know that this is a inversed step problem, I dont quite see the connection in the problems though.

Derivative: 6x -5
What is the antiderivative?
It is 6[(1/2)x^2] -5x
= 3x^2 -5x

Derivative: 6x -5
What is the integral?
INT[6x -5]dx = (6/2)x^2 -5x +C
= 3x^2 -5x +C

p.s. again, i am sorry if i may seem stupid. in fact, your problem is familiar to mine. our teacher decided to give up on us and let us teach ourselves and we have to teach her also, and that is why i am here. my first expression of this site though, its amazing. thank you again!

5. The rule for integral you are trying to take is

$nx^p$

n being the coefficent and p being the power.

So you do this

$\frac{nx^{p+1}}{p +1} + C$