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

The integral from 0 to 1 of (x-1)/(sqrt(x)) is -4/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of (x-1)/(sqrt(x))

\int_{0}^{1} \frac{x - 1}{x} d x

- \frac{4}{3}

Decimal

- 1.33333 \dots

Solution steps

\int_{0}^{1} \frac{x - 1}{x} d x

Expand

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

= \int_{0}^{1} 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_{0}^{1} x d x - \int_{0}^{1} \frac{1}{x} d x

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

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

= \frac{2}{3} - 2

Simplify

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

= - \frac{4}{3}

g (x) = - 3 x^{2} + 5 x - 6

6 x

\int \frac{( x - 1 )}{2} d x

(8 + x) y^{^{'}} = 7 y

\frac{\partial}{\partial x} (ln (x^{2} + y^{4}) - z)

What is the integral from 0 to 1 of (x-1)/(sqrt(x)) ?
The integral from 0 to 1 of (x-1)/(sqrt(x)) is -4/3