What is the integral from 2 to 4 of-x^3+7x^2-14x+8 ?

The integral from 2 to 4 of-x^3+7x^2-14x+8 is 8/3

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integral from 2 to 4 of-x^3+7x^2-14x+8

\int_{2}^{4} - x^{3} + 7 x^{2} - 14 x + 8 d x

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

\int_{2}^{4} - x^{3} + 7 x^{2} - 14 x + 8 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_{2}^{4} x^{3} d x + \int_{2}^{4} 7 x^{2} d x - \int_{2}^{4} 14 x d x + \int_{2}^{4} 8 d x

\int_{2}^{4} x^{3} d x = 60

\int_{2}^{4} 7 x^{2} d x = \frac{392}{3}

\int_{2}^{4} 14 x d x = 84

\int_{2}^{4} 8 d x = 16

= - 60 + \frac{392}{3} - 84 + 16

Simplify

- 60 + \frac{392}{3} - 84 + 16 : \frac{8}{3}

= \frac{8}{3}

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What is the integral from 2 to 4 of-x^3+7x^2-14x+8 ?
The integral from 2 to 4 of-x^3+7x^2-14x+8 is 8/3