What is the integral from 2 to 3 of xsqrt(x-2) ?

The integral from 2 to 3 of xsqrt(x-2) is 26/15

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integral from 2 to 3 of xsqrt(x-2)

\int_{2}^{3} x x - 2 d x

\frac{26}{15}

Decimal

1.73333 \dots

Solution steps

\int_{2}^{3} x x - 2 d x

Apply u-substitution

: \int_{0}^{1} (u + 2) u d u

= \int_{0}^{1} (u + 2) u d u

Expand

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

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

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

\int_{0}^{1} 2 u d u = \frac{4}{3}

= \frac{2}{5} + \frac{4}{3}

Simplify

\frac{2}{5} + \frac{4}{3} : \frac{26}{15}

= \frac{26}{15}

\int_{5}^{8} (x - 6)^{2} d x

\frac{d}{d x} (8 sec (x) tan (x))

\frac{\partial}{\partial z} (22 cos (x) y z^{2})

\int - \frac{1}{16} sin (4 x) d x

x \to 64 lim (x^{\frac{4}{3}})

What is the integral from 2 to 3 of xsqrt(x-2) ?
The integral from 2 to 3 of xsqrt(x-2) is 26/15