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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\int_{0}^{1} (1 - x) d x

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

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

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

= 1 - \frac{2}{3}

Simplify

1 - \frac{2}{3} : \frac{1}{3}

= \frac{1}{3}

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