What is the integral from 2 to 4 of xsqrt(x-2) ?

The integral from 2 to 4 of xsqrt(x-2) is (64sqrt(2))/(15)

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integral from 2 to 4 of xsqrt(x-2)

\int_{2}^{4} x x - 2 d x

\frac{64 2}{15}

Decimal

6.03397 \dots

Solution steps

\int_{2}^{4} x x - 2 d x

Apply u-substitution

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

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

Expand

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

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

\int_{0}^{2} u^{\frac{3}{2}} d u = \frac{8 2}{5}

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

= \frac{8 2}{5} + \frac{8 2}{3}

Simplify

\frac{8 2}{5} + \frac{8 2}{3} : \frac{64 2}{15}

= \frac{64 2}{15}

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What is the integral from 2 to 4 of xsqrt(x-2) ?
The integral from 2 to 4 of xsqrt(x-2) is (64sqrt(2))/(15)