What is the integral from 7 to 10 of (7-x)(x-10) ?

The integral from 7 to 10 of (7-x)(x-10) is 9/2

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integral from 7 to 10 of (7-x)(x-10)

\int_{7}^{10} (7 - x) (x - 10) d x

\frac{9}{2}

Decimal

4.5

Solution steps

\int_{7}^{10} (7 - x) (x - 10) d x

Expand

(7 - x) (x - 10) : 17 x - x^{2} - 70

= \int_{7}^{10} 17 x - x^{2} - 70 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_{7}^{10} 17 x d x - \int_{7}^{10} x^{2} d x - \int_{7}^{10} 70 d x

\int_{7}^{10} 17 x d x = \frac{867}{2}

\int_{7}^{10} x^{2} d x = 219

\int_{7}^{10} 70 d x = 210

= \frac{867}{2} - 219 - 210

Simplify

\frac{867}{2} - 219 - 210 : \frac{9}{2}

= \frac{9}{2}

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What is the integral from 7 to 10 of (7-x)(x-10) ?
The integral from 7 to 10 of (7-x)(x-10) is 9/2