What is the integral from 1 to 2 of ((2-x)sqrt(x)) ?

The integral from 1 to 2 of ((2-x)sqrt(x)) is (16sqrt(2)-14)/(15)

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integral from 1 to 2 of ((2-x)sqrt(x))

\int_{1}^{2} ((2 - x) x) d x

\frac{16 2 - 14}{15}

Decimal

0.57516 \dots

Solution steps

\int_{1}^{2} (2 - x) x d x

Expand

(2 - x) x : 2 x - x^{\frac{3}{2}}

= \int_{1}^{2} 2 x - x^{\frac{3}{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} 2 x d x - \int_{1}^{2} x^{\frac{3}{2}} d x

\int_{1}^{2} 2 x d x = \frac{2 ( 4 2 - 2 )}{3}

\int_{1}^{2} x^{\frac{3}{2}} d x = \frac{8 2 - 2}{5}

= \frac{2 ( 4 2 - 2 )}{3} - \frac{8 2 - 2}{5}

Simplify

\frac{2 ( 4 2 - 2 )}{3} - \frac{8 2 - 2}{5} : \frac{16 2 - 14}{15}

= \frac{16 2 - 14}{15}

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What is the integral from 1 to 2 of ((2-x)sqrt(x)) ?
The integral from 1 to 2 of ((2-x)sqrt(x)) is (16sqrt(2)-14)/(15)