What is the integral from 3 to 8 of (3-x)(x-8) ?

The integral from 3 to 8 of (3-x)(x-8) is 125/6

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integral from 3 to 8 of (3-x)(x-8)

\int_{3}^{8} (3 - x) (x - 8) d x

\frac{125}{6}

Decimal

20.83333 \dots

Solution steps

\int_{3}^{8} (3 - x) (x - 8) d x

Expand

(3 - x) (x - 8) : 11 x - x^{2} - 24

= \int_{3}^{8} 11 x - x^{2} - 24 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_{3}^{8} 11 x d x - \int_{3}^{8} x^{2} d x - \int_{3}^{8} 24 d x

\int_{3}^{8} 11 x d x = \frac{605}{2}

\int_{3}^{8} x^{2} d x = \frac{485}{3}

\int_{3}^{8} 24 d x = 120

= \frac{605}{2} - \frac{485}{3} - 120

Simplify

\frac{605}{2} - \frac{485}{3} - 120 : \frac{125}{6}

= \frac{125}{6}

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What is the integral from 3 to 8 of (3-x)(x-8) ?
The integral from 3 to 8 of (3-x)(x-8) is 125/6