What is the integral from 2 to 9 of (2-x)(x-9) ?

The integral from 2 to 9 of (2-x)(x-9) is 343/6

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integral from 2 to 9 of (2-x)(x-9)

\int_{2}^{9} (2 - x) (x - 9) d x

\frac{343}{6}

Decimal

57.16666 \dots

Solution steps

\int_{2}^{9} (2 - x) (x - 9) d x

Expand

(2 - x) (x - 9) : 11 x - x^{2} - 18

= \int_{2}^{9} 11 x - x^{2} - 18 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}^{9} 11 x d x - \int_{2}^{9} x^{2} d x - \int_{2}^{9} 18 d x

\int_{2}^{9} 11 x d x = \frac{847}{2}

\int_{2}^{9} x^{2} d x = \frac{721}{3}

\int_{2}^{9} 18 d x = 126

= \frac{847}{2} - \frac{721}{3} - 126

Simplify

\frac{847}{2} - \frac{721}{3} - 126 : \frac{343}{6}

= \frac{343}{6}

What is the integral from 2 to 9 of (2-x)(x-9) ?
The integral from 2 to 9 of (2-x)(x-9) is 343/6