What is the integral from 0 to 24 of x^2(1/288 x) ?

The integral from 0 to 24 of x^2(1/288 x) is 288

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integral from 0 to 24 of x^2(1/288 x)

\int_{0}^{24} x^{2} (\frac{1}{288} x) d x

288

Solution steps

\int_{0}^{24} x^{2} \frac{1}{288} x d x

Take the constant out:

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

= \frac{1}{288} \cdot \int_{0}^{24} x^{2} x d x

Simplify

x^{2} x : x^{3}

= \frac{1}{288} \cdot \int_{0}^{24} x^{3} d x

Apply the Power Rule

= \frac{1}{288} [\frac{x ^{4}}{4}]_{0}^{24}

Compute the boundaries:

82944

= \frac{1}{288} \cdot 82944

Simplify

= 288

What is the integral from 0 to 24 of x^2(1/288 x) ?
The integral from 0 to 24 of x^2(1/288 x) is 288