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

∫x^{2} dx = $\dfrac{x^3}{3}$ +C.

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

## Integration of x^{2}

**Answer:** The integral of x square is ∫x^{2} dx = x^{3}/3+C.

**Explanation:**

To find the integration of x^{2}, we will use the power rule of integration formula:

∫x^{n} dx = $\dfrac{x^{n+1}}{n+1}$ +C

with n=2.

So the integration of x^2 will be

∫x^{2} dx = $\dfrac{x^{2+1}}{2+1}$ +C

⇒ ∫x^{2} dx = $\dfrac{x^{3}}{3}$ +C

So the integration of x^{2} is equal to x^{3}/3+C where C is an arbitrary constant, and this is obtained by the power rule of integration.

**You Can Read:** Integration of x^{n}

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## Definite Integral of x^{2}

**Question:** Find the definite integral of x^{2} from 0 to 1, that is, find ∫_{0}^{1} x^{2} dx.

**Answer**

∫_{0}^{1} x^{2} dx = 1/3.

We have:

∫_{0}^{1} x^{2} dx = [ x^{3}/3 ]_{0}^{1} = 1^{3}/3 – 0^{3}/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

## FAQs

### Q1: What is the integral of x^2?

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