What is the integral from 2 to 5 of (sqrt(x)-2)^2 ?

The integral from 2 to 5 of (sqrt(x)-2)^2 is 45/2-(4(10sqrt(5)-4sqrt(2)))/3

integral from 2 to 5 of (sqrt(x)-2)^2

\int_{2}^{5} (x - 2)^{2} d x

\frac{45}{2} - \frac{4 ( 10 5 - 4 2 )}{3}

Decimal

0.22823 \dots

Solution steps

\int_{2}^{5} (x - 2)^{2} d x

Expand

(x - 2)^{2} : x - 4 x + 4

= \int_{2}^{5} x - 4 x + 4 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_{2}^{5} x d x - \int_{2}^{5} 4 x d x + \int_{2}^{5} 4 d x

\int_{2}^{5} x d x = \frac{21}{2}

\int_{2}^{5} 4 x d x = \frac{4 ( 10 5 - 4 2 )}{3}

\int_{2}^{5} 4 d x = 12

= \frac{21}{2} - \frac{4 ( 10 5 - 4 2 )}{3} + 12

Combine the fractions

12 + \frac{21}{2} : \frac{45}{2}

= \frac{45}{2} - \frac{4 ( 10 5 - 4 2 )}{3}

x \to \infty lim (\frac{2}{x} - 3)

x \to 2 lim (4 x^{2})

\frac{d}{d x} (e^{x^{2} - 4} + 4 x + 11)

\int (ln (7 x))^{2} d x

\int_{0}^{x^{2}} e^{t^{2}} d t

What is the integral from 2 to 5 of (sqrt(x)-2)^2 ?
The integral from 2 to 5 of (sqrt(x)-2)^2 is 45/2-(4(10sqrt(5)-4sqrt(2)))/3