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

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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 Notation

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}

\int_{0}^{5} \frac{40}{x ^{2} + 25} d x

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

\frac{1}{1 + e ^{- x}}

\int \frac{2 x + 1}{x ^{2} + 2 x + 82} d x

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

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