Saturday

August 23, 2014

August 23, 2014

Posted by **Me** on Thursday, December 7, 2006 at 2:58pm.

how would I find the most general antiderivative of the function. I also have to check my answer by differentiation.

Would I have to find the derivative first? (I got 12x -8)

What are the steps to solving a problem like this?

No, don't do the derivative first. Do that on the integral, to check your answer.

I use the word "integral" for what you are calling "antiderivative". You can say I am old-fashioned, but I don't see a need for a longer word.

The general rule for integrating any

a x^n term

is that the integral is

a x^(n+1)/(n+1)

When you have a polynomial, as you do here, the integral is the sum of the integrals of the terms.

The first term of the integral is

6 x^3/3 = 2 x^3. Take the derivative of that and you get the original 6 x^2 back, so it is the right answer.

Now you do the other terms, and add them up.

Remember that the most general integral has an arbitrary constant term added.

**Related Questions**

Calculus Help and Check - 1)Find the most general antiderivative of the function...

Math - Find the most general antiderivative of the function. (Check your answer ...

calculus - Find the most general antiderivative of the function 1) f(x)= (X^3)^1...

calculus - find the most general antiderivative of the function f(t)=8t-3sec^2t

Calculus 1 - Find the most general antiderivative of the function. Use C for any...

Math - Calculus Question. - hey can someone explain to me the relationship ...

derivative am i right or wrong - what is the antiderivative of 1/(x^2-2x+2)? ...

math/ check! - find the general term that describes the following sequens 600,...

Cal 1 - Find the most general antiderivative of the function. Use C for any ...

Calculus (Antiderivatives) - What is the antiderivative of the followring ...