Question

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

I don't even know where to start

Answer 1

`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`

Answer 2

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`