What is the integral from 0 to 54 of x(1/1458 x) ?

The integral from 0 to 54 of x(1/1458 x) is 36

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integral from 0 to 54 of x(1/1458 x)

\int_{0}^{54} x (\frac{1}{1458} x) d x

36

Solution steps

\int_{0}^{54} x \frac{1}{1458} x d x

Take the constant out:

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

= \frac{1}{1458} \cdot \int_{0}^{54} xx d x

Simplify

xx : x^{2}

= \frac{1}{1458} \cdot \int_{0}^{54} x^{2} d x

Apply the Power Rule

= \frac{1}{1458} [\frac{x ^{3}}{3}]_{0}^{54}

Compute the boundaries:

52488

= \frac{1}{1458} \cdot 52488

Simplify

= 36

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What is the integral from 0 to 54 of x(1/1458 x) ?
The integral from 0 to 54 of x(1/1458 x) is 36