integrate x^2 between 0 and 2 — step-by-step solution

Let's compute the integral:

\int_{0}^{2} x^{2} d x

ⓘ For constant

n

with

n \neq -1

\frac{x^{n + 1}}{n + 1}

is an antiderivative of

x^{n}

\int x^{2} d x

\frac{x^{3}}{3}

▷

\frac{x^{3}}{3}

Let's evaluate for the interval

[0, 2]

\frac{2^{3}}{3} - \frac{0^{3}}{3}

ⓘ Calculate powers before multiplications, additions and subtractions. With a positive integer exponent, a power corresponds to a repeated product:

2^{3}

2 \cdot 2 \cdot 2

8

\frac{8}{3} + 0

ⓘ Adding 0 changes nothing:

\frac{8}{3} + 0

\frac{8}{3}

▶Integral:

\frac{8}{3}

The numeric value of:

\frac{8}{3}

equals:

▷

\approx 2.6667