What is the integral from 3 to 6 of (3-x)(x-6) ?

The integral from 3 to 6 of (3-x)(x-6) is 9/2

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integral from 3 to 6 of (3-x)(x-6)

\int_{3}^{6} (3 - x) (x - 6) d x

\frac{9}{2}

Decimal

4.5

Solution steps

\int_{3}^{6} (3 - x) (x - 6) d x

Expand

(3 - x) (x - 6) : 9 x - x^{2} - 18

= \int_{3}^{6} 9 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_{3}^{6} 9 x d x - \int_{3}^{6} x^{2} d x - \int_{3}^{6} 18 d x

\int_{3}^{6} 9 x d x = \frac{243}{2}

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} 18 d x = 54

= \frac{243}{2} - 63 - 54

Simplify

\frac{243}{2} - 63 - 54 : \frac{9}{2}

= \frac{9}{2}

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What is the integral from 3 to 6 of (3-x)(x-6) ?
The integral from 3 to 6 of (3-x)(x-6) is 9/2