What is the integral from 0 to 1 of ax^3 ?

The integral from 0 to 1 of ax^3 is a/4

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integral from 0 to 1 of ax^3

\int_{0}^{1} a x^{3} d x

\frac{a}{4}

Solution steps

\int_{0}^{1} a x^{3} d x

Take the constant out:

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

= a \cdot \int_{0}^{1} x^{3} d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{4}

= a \frac{1}{4}

Simplify

= \frac{a}{4}

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What is the integral from 0 to 1 of ax^3 ?
The integral from 0 to 1 of ax^3 is a/4