What is the integral from 4 to 6 of (x^2-2x-8) ?

The integral from 4 to 6 of (x^2-2x-8) is 44/3

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integral from 4 to 6 of (x^2-2x-8)

\int_{4}^{6} (x^{2} - 2 x - 8) d x

\frac{44}{3}

Decimal

14.66666 \dots

Solution steps

\int_{4}^{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_{4}^{6} x^{2} d x - \int_{4}^{6} 2 x d x - \int_{4}^{6} 8 d x

\int_{4}^{6} x^{2} d x = \frac{152}{3}

\int_{4}^{6} 2 x d x = 20

\int_{4}^{6} 8 d x = 16

= \frac{152}{3} - 20 - 16

Simplify

\frac{152}{3} - 20 - 16 : \frac{44}{3}

= \frac{44}{3}

\int_{1}^{2} 16 x d x

\int_{- 1}^{0} (x^{3} - 2)^{2} \cdot 3 x^{2} d x

\int_{0}^{4} 2 t^{2} + t^{\frac{3}{2}} d t

\int_{6}^{7} (x x - 6) d x

\int_{1}^{x^{2}} 2 x^{2} y (x + y) d y

What is the integral from 4 to 6 of (x^2-2x-8) ?
The integral from 4 to 6 of (x^2-2x-8) is 44/3