What is the integral from 2 to 4 of x^2-2x-8 ?

The integral from 2 to 4 of x^2-2x-8 is -28/3

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integral from 2 to 4 of x^2-2x-8

\int_{2}^{4} x^{2} - 2 x - 8 d x

- \frac{28}{3}

Decimal Notation

- 9.33333 \dots

Solution steps

\int_{2}^{4} x^{2} - 2 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^{2} d x - \int_{2}^{4} 2 x d x - \int_{2}^{4} 8 d x

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 2 x d x = 12

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

= \frac{56}{3} - 12 - 16

Simplify

\frac{56}{3} - 12 - 16 : - \frac{28}{3}

= - \frac{28}{3}

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What is the integral from 2 to 4 of x^2-2x-8 ?
The integral from 2 to 4 of x^2-2x-8 is -28/3