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

The integral from 0 to 1 of-(x-1) is 1/2

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-(x-1)

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

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

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

= - (\frac{1}{2} - 1)

Simplify

- (\frac{1}{2} - 1) : \frac{1}{2}

= \frac{1}{2}

What is the integral from 0 to 1 of-(x-1) ?
The integral from 0 to 1 of-(x-1) is 1/2