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

The integral from 0 to 2 of (2-x)sqrt(x) is (16sqrt(2))/(15)

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

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

\frac{16 2}{15}

Decimal

1.50849 \dots

Solution steps

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

Expand

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

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

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

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

= \frac{8 2}{3} - \frac{8 2}{5}

Simplify

\frac{8 2}{3} - \frac{8 2}{5} : \frac{16 2}{15}

= \frac{16 2}{15}

\frac{\partial}{\partial x} (e^{2 x yz - 1})

\frac{d}{d x} (e^{2 x} + 4)

\int_{0}^{4} (x + 3 x) d x

\int e^{x} e^{x} + 5 d x

\frac{d y}{d x} = (x + y)^{2}

What is the integral from 0 to 2 of (2-x)sqrt(x) ?
The integral from 0 to 2 of (2-x)sqrt(x) is (16sqrt(2))/(15)