What is the integral from 4 to 11 of (4-x)(x-11) ?

The integral from 4 to 11 of (4-x)(x-11) is 343/6

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integral from 4 to 11 of (4-x)(x-11)

\int_{4}^{11} (4 - x) (x - 11) d x

\frac{343}{6}

Decimal

57.16666 \dots

Solution steps

\int_{4}^{11} (4 - x) (x - 11) d x

Expand

(4 - x) (x - 11) : 15 x - x^{2} - 44

= \int_{4}^{11} 15 x - x^{2} - 44 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}^{11} 15 x d x - \int_{4}^{11} x^{2} d x - \int_{4}^{11} 44 d x

\int_{4}^{11} 15 x d x = \frac{1575}{2}

\int_{4}^{11} x^{2} d x = \frac{1267}{3}

\int_{4}^{11} 44 d x = 308

= \frac{1575}{2} - \frac{1267}{3} - 308

Simplify

\frac{1575}{2} - \frac{1267}{3} - 308 : \frac{343}{6}

= \frac{343}{6}

What is the integral from 4 to 11 of (4-x)(x-11) ?
The integral from 4 to 11 of (4-x)(x-11) is 343/6