What is the integral from 0 to 12 of x(1/72 x) ?

The integral from 0 to 12 of x(1/72 x) is 8

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integral from 0 to 12 of x(1/72 x)

\int_{0}^{12} x (\frac{1}{72} x) d x

8

Solution steps

\int_{0}^{12} x \frac{1}{72} x d x

Take the constant out:

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

= \frac{1}{72} \cdot \int_{0}^{12} xx d x

Simplify

xx : x^{2}

= \frac{1}{72} \cdot \int_{0}^{12} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{12}

= \frac{1}{72} [\frac{x ^{3}}{3}]_{0}^{12}

Compute the boundaries:

576

= \frac{1}{72} \cdot 576

Simplify

= 8

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What is the integral from 0 to 12 of x(1/72 x) ?
The integral from 0 to 12 of x(1/72 x) is 8