What is the integral from 1 to 5 of (x^2-2x-8) ?

The integral from 1 to 5 of (x^2-2x-8) is -44/3

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integral from 1 to 5 of (x^2-2x-8)

\int_{1}^{5} (x^{2} - 2 x - 8) d x

- \frac{44}{3}

Decimal

- 14.66666 \dots

Solution steps

\int_{1}^{5} 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_{1}^{5} x^{2} d x - \int_{1}^{5} 2 x d x - \int_{1}^{5} 8 d x

\int_{1}^{5} x^{2} d x = \frac{124}{3}

\int_{1}^{5} 2 x d x = 24

\int_{1}^{5} 8 d x = 32

= \frac{124}{3} - 24 - 32

Simplify

\frac{124}{3} - 24 - 32 : - \frac{44}{3}

= - \frac{44}{3}

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What is the integral from 1 to 5 of (x^2-2x-8) ?
The integral from 1 to 5 of (x^2-2x-8) is -44/3