What is the integral from 0 to 2 of (3-x)sqrt(x) ?

The integral from 0 to 2 of (3-x)sqrt(x) is 4sqrt(2)-(8sqrt(2))/5

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integral from 0 to 2 of (3-x)sqrt(x)

\int_{0}^{2} (3 - x) x d x

42 - \frac{8 2}{5}

Decimal

3.39411 \dots

Solution steps

\int_{0}^{2} (3 - x) x d x

Expand

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

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

\int_{0}^{2} 3 x d x = 42

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

= 42 - \frac{8 2}{5}

\int_{0}^{π} x^{4} cos (n x) d x

\int_{- 6}^{- 1} (x^{- 1} + 5 x) d x

\int_{- 2}^{0} \frac{15}{64} + \frac{x}{64} d x

\int_{- 1}^{1} (3 x - 5) d x

\int_{- 1}^{1} (9 x^{2} + 5 z + 4 x y) d z

What is the integral from 0 to 2 of (3-x)sqrt(x) ?
The integral from 0 to 2 of (3-x)sqrt(x) is 4sqrt(2)-(8sqrt(2))/5