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

The integral from 1 to 4 of (x-1)/(sqrt(x)) is 8/3

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

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

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

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

Expand

\frac{x - 1}{x} : x - \frac{1}{x}

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

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

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

= \frac{14}{3} - 2

Simplify

\frac{14}{3} - 2 : \frac{8}{3}

= \frac{8}{3}

\frac{1}{2} + 2 sin (x) + 2 cos (x)

25 y^{^{''}} + 11 y = 0

x \to 2 - lim (\frac{1}{x ^{2} - 9})

\int \frac{- 2 x ^{3} + x}{- 4 x ^{4} + 4 x ^{2}} d x

\int \frac{x}{1 - x ^{3}} d x

What is the integral from 1 to 4 of (x-1)/(sqrt(x)) ?
The integral from 1 to 4 of (x-1)/(sqrt(x)) is 8/3