Find the antiderivative of f'(x)=3x^3?

I don't even know where to start

2 Answers
Feb 26, 2018

#3/4 x^4 +C#

Explanation:

When differentiation #ax^b# you multiply the coefficient of the x term by the power and then reduce the power by 1. In this case #ab x^(b-1)#.

An antiderivative is the opposite of this to increase the power by 1 and then divide the coefficient by the new power. So for your example, that would be #3/4 x^4#. However, we do not know if there was a constant when integrating (another name for antiderivative) so we write #+C#

Feb 26, 2018

Read below

Explanation:

The anti power rule states that:

#intx^ndx=x^(n+1)/(n+1)#

Therefore, #int3x^3dx# is:

#(3x^(3+1))/(3+1)=>(3x^4)/4+C#