What is the integral from 2 to 5 of (2-x)(x-5) ?

The integral from 2 to 5 of (2-x)(x-5) is 9/2

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integral from 2 to 5 of (2-x)(x-5)

\int_{2}^{5} (2 - x) (x - 5) d x

\frac{9}{2}

Decimal

4.5

Solution steps

\int_{2}^{5} (2 - x) (x - 5) d x

Expand

(2 - x) (x - 5) : 7 x - x^{2} - 10

= \int_{2}^{5} 7 x - x^{2} - 10 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}^{5} 7 x d x - \int_{2}^{5} x^{2} d x - \int_{2}^{5} 10 d x

\int_{2}^{5} 7 x d x = \frac{147}{2}

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 10 d x = 30

= \frac{147}{2} - 39 - 30

Simplify

\frac{147}{2} - 39 - 30 : \frac{9}{2}

= \frac{9}{2}

What is the integral from 2 to 5 of (2-x)(x-5) ?
The integral from 2 to 5 of (2-x)(x-5) is 9/2