What is the integral from 0 to 4 of x^2*x/8 ?

The integral from 0 to 4 of x^2*x/8 is 8

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integral from 0 to 4 of x^2*x/8

\int_{0}^{4} x^{2} \cdot \frac{x}{8} d x

8

Solution steps

\int_{0}^{4} x^{2} \frac{x}{8} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{4} x^{2} x d x

Simplify

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

= \frac{1}{8} \cdot \int_{0}^{4} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{4}

= \frac{1}{8} [\frac{x ^{4}}{4}]_{0}^{4}

Compute the boundaries:

64

= \frac{1}{8} \cdot 64

Simplify

= 8

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What is the integral from 0 to 4 of x^2*x/8 ?
The integral from 0 to 4 of x^2*x/8 is 8