What is the integral from 9 to 18 of xsqrt(x-9) ?

The integral from 9 to 18 of xsqrt(x-9) is 1296/5

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integral from 9 to 18 of xsqrt(x-9)

\int_{9}^{18} x x - 9 d x

\frac{1296}{5}

Decimal

259.2

Solution steps

\int_{9}^{18} x x - 9 d x

Apply u-substitution

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

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

Expand

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

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

\int_{0}^{9} u^{\frac{3}{2}} d u = \frac{486}{5}

\int_{0}^{9} 9 u d u = 162

= \frac{486}{5} + 162

Simplify

\frac{486}{5} + 162 : \frac{1296}{5}

= \frac{1296}{5}

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What is the integral from 9 to 18 of xsqrt(x-9) ?
The integral from 9 to 18 of xsqrt(x-9) is 1296/5