en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 1 of |x-1|

Solution

\int_{- 1}^{1} ∣ x - 1 ∣ d x

Solution

2

Solution steps

\int_{- 1}^{1} ∣ x - 1 ∣ d x

Eliminate Absolutes

= \int_{- 1}^{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_{- 1}^{1} x d x + \int_{- 1}^{1} 1 d x

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

\int_{- 1}^{1} 1 d x = 2

= - 0 + 2

Simplify

= 2

Popular Examples

integral from 0 to 2pi of x^2sin(x)

\int_{0}^{2 π} x^{2} sin (x) d x

integral from 0 to (5pi)/6 of sin(x)

\int_{0}^{\frac{5 π}{6}} sin (x) d x

integral from 0 to 1 of 8cos((pix)/2)

\int_{0}^{1} 8 cos (\frac{π x}{2}) d x

integral from 0 to 1 of (x^2+x-1)

\int_{0}^{1} (x^{2} + x - 1) d x

integral from 0 to 2pi of cos(nx)

\int_{0}^{2 π} cos (n x) d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of |x-1| ?
The integral from-1 to 1 of |x-1| is 2