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

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

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integral from b to a of x^2

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

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

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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