What is the integral from a to b of (x^2) ?

The integral from a to b of (x^2) is (b^3-a^3)/3

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integral from a to b of (x^2)

\int_{a}^{b} (x^{2}) d x

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

Solution steps

\int_{a}^{b} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{a}^{b}

= [\frac{x ^{3}}{3}]_{a}^{b}

Compute the boundaries:

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

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

Simplify

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

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What is the integral from a to b of (x^2) ?
The integral from a to b of (x^2) is (b^3-a^3)/3