What is the integral from 1 to a of x^2 ?

The integral from 1 to a of x^2 is (a^3-1)/3

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integral from 1 to a of x^2

\int_{1}^{a} x^{2} d x

\frac{a ^{3} - 1}{3}

Solution steps

\int_{1}^{a} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{a}

= [\frac{x ^{3}}{3}]_{1}^{a}

Compute the boundaries:

\frac{a ^{3}}{3} - \frac{1}{3}

= \frac{a ^{3}}{3} - \frac{1}{3}

Simplify

= \frac{a ^{3} - 1}{3}

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What is the integral from 1 to a of x^2 ?
The integral from 1 to a of x^2 is (a^3-1)/3