Integral of x^2 | How to Integrate x^2? [Solved]

The integral of x^2 (x square) is equal to x3/3+C where C is a constant. The integration formula of x2 (x square) is given by

∫x2 dx = $\dfrac{x^3}{3}$ +C.

Integral of x^2

Let us now learn how to integrate x^2 dx.

Integration of x2

Answer: The integral of x square is ∫x2 dx = x3/3+C.

Explanation:

To find the integration of x2, we will use the power rule of integration formula:

∫xn dx = $\dfrac{x^{n+1}}{n+1}$ +C

with n=2.

So the integration of x^2 will be

∫x2 dx = $\dfrac{x^{2+1}}{2+1}$ +C

⇒ ∫x2 dx = $\dfrac{x^{3}}{3}$ +C

So the integration of x2 is equal to x3/3+C where C is an arbitrary constant, and this is obtained by the power rule of integration.

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Definite Integral of x2

Question: Find the definite integral of x2 from 0 to 1, that is, find ∫01 x2 dx.

Answer

01 x2 dx = 1/3.

We have:

01 x2 dx = [ x3/3 ]01 = 13/3 – 03/3 = 1-0 = 1.

So the definite integration of x^2 from 0 to 1 is equal to 1/3.

Read Also: Integration of 1/x

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FAQs

Q1: What is the integral of x^2?

Answer: The integral of x square is equal to x3/3+C where C is an integral constant.

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