What is the integral from 8 to 9 of xsqrt(x-8) ?

The integral from 8 to 9 of xsqrt(x-8) is 86/15

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integral from 8 to 9 of xsqrt(x-8)

\int_{8}^{9} x x - 8 d x

\frac{86}{15}

Decimal

5.73333 \dots

Solution steps

\int_{8}^{9} x x - 8 d x

Apply u-substitution

= \int_{0}^{1} (u + 8) u d u

Expand

(u + 8) u : u^{\frac{3}{2}} + 8 u

= \int_{0}^{1} u^{\frac{3}{2}} + 8 u d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 8 u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} 8 u d u = \frac{16}{3}

= \frac{2}{5} + \frac{16}{3}

Simplify

\frac{2}{5} + \frac{16}{3} : \frac{86}{15}

= \frac{86}{15}

What is the integral from 8 to 9 of xsqrt(x-8) ?
The integral from 8 to 9 of xsqrt(x-8) is 86/15