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

I don't even know where to start

Answer 1

#3/4 x^4 +C#

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#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Read below

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#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

The antiderivative of ( f'(x) = 3x^3 ) is ( f(x) = \frac{3}{4}x^4 + C ), where ( C ) is the constant of integration.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7