What is the integral from 1 to 3 of ((2x^3)/3+5) ?

The integral from 1 to 3 of ((2x^3)/3+5) is 70/3

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integral from 1 to 3 of ((2x^3)/3+5)

\int_{1}^{3} (\frac{2 x ^{3}}{3} + 5) d x

\frac{70}{3}

Decimal

23.33333 \dots

Solution steps

\int_{1}^{3} \frac{2 x ^{3}}{3} + 5 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_{1}^{3} \frac{2 x ^{3}}{3} d x + \int_{1}^{3} 5 d x

\int_{1}^{3} \frac{2 x ^{3}}{3} d x = \frac{40}{3}

\int_{1}^{3} 5 d x = 10

= \frac{40}{3} + 10

Simplify

\frac{40}{3} + 10 : \frac{70}{3}

= \frac{70}{3}

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What is the integral from 1 to 3 of ((2x^3)/3+5) ?
The integral from 1 to 3 of ((2x^3)/3+5) is 70/3