What is the integral from 0 to 2 of 4x-(x^3)/3 ?

The integral from 0 to 2 of 4x-(x^3)/3 is 20/3

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integral from 0 to 2 of 4x-(x^3)/3

\int_{0}^{2} 4 x - \frac{x ^{3}}{3} d x

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

\int_{0}^{2} 4 x - \frac{x ^{3}}{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} 4 x d x - \int_{0}^{2} \frac{x ^{3}}{3} d x

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

\int_{0}^{2} \frac{x ^{3}}{3} d x = \frac{4}{3}

= 8 - \frac{4}{3}

Simplify

8 - \frac{4}{3} : \frac{20}{3}

= \frac{20}{3}

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What is the integral from 0 to 2 of 4x-(x^3)/3 ?
The integral from 0 to 2 of 4x-(x^3)/3 is 20/3