What is the integral from 0 to 3 of (3-x)sqrt(x) ?

The integral from 0 to 3 of (3-x)sqrt(x) is 6sqrt(3)-(18sqrt(3))/5

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integral from 0 to 3 of (3-x)sqrt(x)

\int_{0}^{3} (3 - x) x d x

63 - \frac{18 3}{5}

Decimal Notation

4.15692 \dots

Solution steps

\int_{0}^{3} (3 - x) x d x

Expand

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

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

\int_{0}^{3} 3 x d x = 63

\int_{0}^{3} x^{\frac{3}{2}} d x = \frac{18 3}{5}

= 63 - \frac{18 3}{5}

\frac{d}{d y} (x (y) z (y))

x e^{x^{2}}, 0

\int \frac{21}{4 + 25 r ^{2}} d r

\frac{- 1}{( x - 1 ) ^{2}}

\frac{d}{d x} (\frac{x ^{4} - 2}{x ^{2} - 2})

What is the integral from 0 to 3 of (3-x)sqrt(x) ?
The integral from 0 to 3 of (3-x)sqrt(x) is 6sqrt(3)-(18sqrt(3))/5