What is the integral from 0 to 3 of 4pi((x^3)/3) ?

The integral from 0 to 3 of 4pi((x^3)/3) is 27pi

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integral from 0 to 3 of 4pi((x^3)/3)

\int_{0}^{3} 4 π (\frac{x ^{3}}{3}) d x

27 π

Decimal

84.82300 \dots

Solution steps

\int_{0}^{3} 4 π \frac{x ^{3}}{3} d x

Take the constant out:

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

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

4 π \frac{1}{3} = \frac{4 π}{3}

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

Apply the Power Rule

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

Compute the boundaries:

\frac{81}{4}

= \frac{4 π}{3} \cdot \frac{81}{4}

Simplify

= 27 π

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