What is the integral from 0 to 2 of (x^2)/8 ?

The integral from 0 to 2 of (x^2)/8 is 1/3

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integral from 0 to 2 of (x^2)/8

\int_{0}^{2} \frac{x ^{2}}{8} d x

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\int_{0}^{2} \frac{x ^{2}}{8} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

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

= \frac{1}{8} [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= \frac{1}{8} \cdot \frac{8}{3}

Simplify

= \frac{1}{3}

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What is the integral from 0 to 2 of (x^2)/8 ?
The integral from 0 to 2 of (x^2)/8 is 1/3