What is the integral from 1 to 4 of (x-2)/(sqrt(x)) ?

The integral from 1 to 4 of (x-2)/(sqrt(x)) is 2/3

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integral from 1 to 4 of (x-2)/(sqrt(x))

\int_{1}^{4} \frac{x - 2}{x} d x

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

\int_{1}^{4} \frac{x - 2}{x} d x

Expand

\frac{x - 2}{x} : x - \frac{2}{x}

= \int_{1}^{4} x - \frac{2}{x} 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_{1}^{4} x d x - \int_{1}^{4} \frac{2}{x} d x

\int_{1}^{4} x d x = \frac{14}{3}

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

= \frac{14}{3} - 4

Simplify

\frac{14}{3} - 4 : \frac{2}{3}

= \frac{2}{3}

f (x) = 3 arccsc (x)

\int x^{2} sech^{2} (x^{3}) d x

\frac{d}{d x} (x^{3} - 8)

y^{^{'}} + 2 y = 25 sin (x) + 40 cos (x), y (0) = 1

y = x, (9, 3)

What is the integral from 1 to 4 of (x-2)/(sqrt(x)) ?
The integral from 1 to 4 of (x-2)/(sqrt(x)) is 2/3