en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 1 of |x-1|

Solution

\int_{- 2}^{1} ∣ x - 1 ∣ d x

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

\int_{- 2}^{1} ∣ x - 1 ∣ d x

Eliminate Absolutes

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

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

\int_{- 2}^{1} 1 d x = 3

= - (- \frac{3}{2}) + 3

Simplify

- (- \frac{3}{2}) + 3 : \frac{9}{2}

= \frac{9}{2}

Popular Examples

integral from 0 to 1 of 9cos(x^2)

\int_{0}^{1} 9 cos (x^{2}) d x

integral from 2 to 3 of sqrt(1+x^2)

\int_{2}^{3} 1 + x^{2} d x

integral from 0 to 1/9 of xln(9x)

\int_{0}^{\frac{1}{9}} x ln (9 x) d x

integral from 1 to 2 of 1/(x^2-4x-5)

\int_{1}^{2} \frac{1}{x ^{2} - 4 x - 5} d x

integral from 0 to 1 of (cos(x))/(1+x)

\int_{0}^{1} \frac{cos ( x )}{1 + x} d x

Frequently Asked Questions (FAQ)

What is the integral from-2 to 1 of |x-1| ?
The integral from-2 to 1 of |x-1| is 9/2