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

The integral from 2 to 8 of (2-x)(x-8) is 36

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integral from 2 to 8 of (2-x)(x-8)

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

36

Solution steps

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

Expand

(2 - x) (x - 8) : 10 x - x^{2} - 16

= \int_{2}^{8} 10 x - x^{2} - 16 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}^{8} 10 x d x - \int_{2}^{8} x^{2} d x - \int_{2}^{8} 16 d x

\int_{2}^{8} 10 x d x = 300

\int_{2}^{8} x^{2} d x = 168

\int_{2}^{8} 16 d x = 96

= 300 - 168 - 96

Simplify

= 36

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What is the integral from 2 to 8 of (2-x)(x-8) ?
The integral from 2 to 8 of (2-x)(x-8) is 36