What is the integral from 9 to 10 of (xsqrt(x-9)) ?

The integral from 9 to 10 of (xsqrt(x-9)) is 32/5

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integral from 9 to 10 of (xsqrt(x-9))

\int_{9}^{10} (x x - 9) d x

\frac{32}{5}

Decimal

6.4

Solution steps

\int_{9}^{10} x x - 9 d x

Apply u-substitution

= \int_{0}^{1} (u + 9) u d u

Expand

(u + 9) u : u^{\frac{3}{2}} + 9 u

= \int_{0}^{1} u^{\frac{3}{2}} + 9 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} 9 u d u

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

\int_{0}^{1} 9 u d u = 6

= \frac{2}{5} + 6

Simplify

\frac{2}{5} + 6 : \frac{32}{5}

= \frac{32}{5}

What is the integral from 9 to 10 of (xsqrt(x-9)) ?
The integral from 9 to 10 of (xsqrt(x-9)) is 32/5