What is the integral from 1 to 5 of (x^2)/(12) ?

The integral from 1 to 5 of (x^2)/(12) is 31/9

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integral from 1 to 5 of (x^2)/(12)

\int_{1}^{5} \frac{x ^{2}}{12} d x

\frac{31}{9}

Decimal Notation

3.44444 \dots

Solution steps

\int_{1}^{5} \frac{x ^{2}}{12} d x

Take the constant out:

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

= \frac{1}{12} \cdot \int_{1}^{5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{5}

= \frac{1}{12} [\frac{x ^{3}}{3}]_{1}^{5}

Compute the boundaries:

\frac{124}{3}

= \frac{1}{12} \cdot \frac{124}{3}

Simplify

= \frac{31}{9}

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What is the integral from 1 to 5 of (x^2)/(12) ?
The integral from 1 to 5 of (x^2)/(12) is 31/9