What is the integral from 0 to x of (x^2)/2 ?

The integral from 0 to x of (x^2)/2 is (x^3)/6

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integral from 0 to x of (x^2)/2

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

\frac{x ^{3}}{6}

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{x} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{x}

= \frac{1}{2} [\frac{x ^{3}}{3}]_{0}^{x}

Compute the boundaries:

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

= \frac{1}{2} \cdot \frac{x ^{3}}{3}

Simplify

= \frac{x ^{3}}{6}

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What is the integral from 0 to x of (x^2)/2 ?
The integral from 0 to x of (x^2)/2 is (x^3)/6