What is the integral from 0 to 1 of (sqrt(x)-x)^2 ?

The integral from 0 to 1 of (sqrt(x)-x)^2 is 1/30

Popular >

integral from 0 to 1 of (sqrt(x)-x)^2

\int_{0}^{1} (x - x)^{2} d x

\frac{1}{30}

Decimal Notation

0.03333 \dots

Solution steps

\int_{0}^{1} (x - x)^{2} d x

Expand

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

= \int_{0}^{1} x - 2 x^{\frac{3}{2}} + x^{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}^{1} x d x - \int_{0}^{1} 2 x^{\frac{3}{2}} d x + \int_{0}^{1} x^{2} d x

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} 2 x^{\frac{3}{2}} d x = \frac{4}{5}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{1}{2} - \frac{4}{5} + \frac{1}{3}

Simplify

\frac{1}{2} - \frac{4}{5} + \frac{1}{3} : \frac{1}{30}

= \frac{1}{30}

\frac{s - 4}{s ^{2} - 8 s + 10}

t^{\frac{4}{3}}

f (x) = x^{3} - 9 x + 4, (3, 4)

\frac{d y}{d x} = \frac{( x - y )}{( x + y )}

(1 + x)^{- 5}

What is the integral from 0 to 1 of (sqrt(x)-x)^2 ?
The integral from 0 to 1 of (sqrt(x)-x)^2 is 1/30