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

The integral from 0 to 3 of 1/3 x^3 is 27/4

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integral from 0 to 3 of 1/3 x^3

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

\frac{27}{4}

Decimal

6.75

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

= \frac{1}{3} [\frac{x ^{4}}{4}]_{0}^{3}

Compute the boundaries:

\frac{81}{4}

= \frac{1}{3} \cdot \frac{81}{4}

Simplify

= \frac{27}{4}

What is the integral from 0 to 3 of 1/3 x^3 ?
The integral from 0 to 3 of 1/3 x^3 is 27/4