What is the integral from 0 to 2 of (9-x)sqrt(x) ?

The integral from 0 to 2 of (9-x)sqrt(x) is 12sqrt(2)-(8sqrt(2))/5

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integral from 0 to 2 of (9-x)sqrt(x)

\int_{0}^{2} (9 - x) x d x

122 - \frac{8 2}{5}

Decimal

14.70782 \dots

Solution steps

\int_{0}^{2} (9 - x) x d x

Expand

(9 - x) x : 9 x - x^{\frac{3}{2}}

= \int_{0}^{2} 9 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_{0}^{2} 9 x d x - \int_{0}^{2} x^{\frac{3}{2}} d x

\int_{0}^{2} 9 x d x = 122

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

= 122 - \frac{8 2}{5}

What is the integral from 0 to 2 of (9-x)sqrt(x) ?
The integral from 0 to 2 of (9-x)sqrt(x) is 12sqrt(2)-(8sqrt(2))/5