What is the integral from 5 to 11 of (5-x)(x-11) ?

The integral from 5 to 11 of (5-x)(x-11) is 36

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integral from 5 to 11 of (5-x)(x-11)

\int_{5}^{11} (5 - x) (x - 11) d x

36

Solution steps

\int_{5}^{11} (5 - x) (x - 11) d x

Expand

(5 - x) (x - 11) : 16 x - x^{2} - 55

= \int_{5}^{11} 16 x - x^{2} - 55 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_{5}^{11} 16 x d x - \int_{5}^{11} x^{2} d x - \int_{5}^{11} 55 d x

\int_{5}^{11} 16 x d x = 768

\int_{5}^{11} x^{2} d x = 402

\int_{5}^{11} 55 d x = 330

= 768 - 402 - 330

Simplify

= 36

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What is the integral from 5 to 11 of (5-x)(x-11) ?
The integral from 5 to 11 of (5-x)(x-11) is 36