What is the integral from 6 to 11 of 3xsqrt(x-2) ?

The integral from 6 to 11 of 3xsqrt(x-2) is 1646/5

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integral from 6 to 11 of 3xsqrt(x-2)

\int_{6}^{11} 3 x x - 2 d x

\frac{1646}{5}

Decimal

329.2

Solution steps

\int_{6}^{11} 3 x x - 2 d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{6}^{11} x x - 2 d x

Apply u-substitution

: \int_{4}^{9} (u + 2) u d u

= 3 \cdot \int_{4}^{9} (u + 2) u d u

Expand

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

= 3 \cdot \int_{4}^{9} 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

= 3 (\int_{4}^{9} u^{\frac{3}{2}} d u + \int_{4}^{9} 2 u d u)

\int_{4}^{9} u^{\frac{3}{2}} d u = \frac{422}{5}

\int_{4}^{9} 2 u d u = \frac{76}{3}

= 3 (\frac{422}{5} + \frac{76}{3})

Simplify

3 (\frac{422}{5} + \frac{76}{3}) : \frac{1646}{5}

= \frac{1646}{5}

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What is the integral from 6 to 11 of 3xsqrt(x-2) ?
The integral from 6 to 11 of 3xsqrt(x-2) is 1646/5