What is the integral from 0 to 2 of 2x^3+4x^2 ?

The integral from 0 to 2 of 2x^3+4x^2 is 56/3

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integral from 0 to 2 of 2x^3+4x^2

\int_{0}^{2} 2 x^{3} + 4 x^{2} d x

\frac{56}{3}

Decimal

18.66666 \dots

Solution steps

\int_{0}^{2} 2 x^{3} + 4 x^{2} 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} 2 x^{3} d x + \int_{0}^{2} 4 x^{2} d x

\int_{0}^{2} 2 x^{3} d x = 8

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

= 8 + \frac{32}{3}

Simplify

8 + \frac{32}{3} : \frac{56}{3}

= \frac{56}{3}

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What is the integral from 0 to 2 of 2x^3+4x^2 ?
The integral from 0 to 2 of 2x^3+4x^2 is 56/3