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

The integral from 1 to 3 of (x^2)/2 is 13/3

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integral from 1 to 3 of (x^2)/2

\int_{1}^{3} \frac{x ^{2}}{2} d x

\frac{13}{3}

Decimal

4.33333 \dots

Solution steps

\int_{1}^{3} \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_{1}^{3} x^{2} d x

Apply the Power Rule

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

Compute the boundaries:

\frac{26}{3}

= \frac{1}{2} \cdot \frac{26}{3}

Simplify

= \frac{13}{3}

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What is the integral from 1 to 3 of (x^2)/2 ?
The integral from 1 to 3 of (x^2)/2 is 13/3