What is the integral from 0 to 2 of (6-x)sqrt(x) ?

The integral from 0 to 2 of (6-x)sqrt(x) is 8sqrt(2)-(8sqrt(2))/5

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integral from 0 to 2 of (6-x)sqrt(x)

\int_{0}^{2} (6 - x) x d x

82 - \frac{8 2}{5}

Decimal Notation

9.05096 \dots

Solution steps

\int_{0}^{2} (6 - x) x d x

Expand

(6 - x) x : 6 x - x^{\frac{3}{2}}

= \int_{0}^{2} 6 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} 6 x d x - \int_{0}^{2} x^{\frac{3}{2}} d x

\int_{0}^{2} 6 x d x = 82

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

= 82 - \frac{8 2}{5}

\int_{0}^{4} 4 x^{2} - x^{3} d x

x \to 4 + lim (x)

\int \frac{( 12 x + 30 )}{( x ^{2} + 2 x - 8 )} d x

\int \frac{x ^{3}}{x ^{2}} d x

\frac{\partial}{\partial y} (4 x^{3} y^{- 2})

What is the integral from 0 to 2 of (6-x)sqrt(x) ?
The integral from 0 to 2 of (6-x)sqrt(x) is 8sqrt(2)-(8sqrt(2))/5