What is the integral from 1 to 6 of x^2-2x-8 ?

The integral from 1 to 6 of x^2-2x-8 is -10/3

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integral from 1 to 6 of x^2-2x-8

\int_{1}^{6} x^{2} - 2 x - 8 d x

- \frac{10}{3}

Decimal

- 3.33333 \dots

Solution steps

\int_{1}^{6} 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}^{6} x^{2} d x - \int_{1}^{6} 2 x d x - \int_{1}^{6} 8 d x

\int_{1}^{6} x^{2} d x = \frac{215}{3}

\int_{1}^{6} 2 x d x = 35

\int_{1}^{6} 8 d x = 40

= \frac{215}{3} - 35 - 40

Simplify

\frac{215}{3} - 35 - 40 : - \frac{10}{3}

= - \frac{10}{3}

What is the integral from 1 to 6 of x^2-2x-8 ?
The integral from 1 to 6 of x^2-2x-8 is -10/3