integ(x^2,x,[a,b]) — step-by-step solution

Let's compute the integral:

\int_{a}^{b} 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

[a, b]

\frac{b^{3}}{3} - \frac{a^{3}}{3}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{b^{3}}{3} - \frac{a^{3}}{3}

\frac{b^{3} - a^{3}}{3}

▶Integral:

\frac{b^{3} - a^{3}}{3}