en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of |x-1|

Solution

\int_{0}^{3} ∣ x - 1 ∣ d x

Solution

\frac{5}{2}

+1

Decimal Notation

2.5

Solution steps

\int_{0}^{3} ∣ x - 1 ∣ d x

Eliminate Absolutes

= \int_{0}^{1} - x + 1 d x + \int_{1}^{3} x - 1 d x

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

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

= \frac{1}{2} + 2

Simplify

\frac{1}{2} + 2 : \frac{5}{2}

= \frac{5}{2}

Popular Examples

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

\int_{0}^{1} 1 + x^{2} d x

integral from 0 to 5 of pi(2x)^2

\int_{0}^{5} π (2 x)^{2} d x

integral of ((sec^2(x)))/(tan^2(x))

\int \frac{( sec ^{2} ( x ) )}{tan ^{2} ( x )} d x

derivative of y=(1/(cos^2(x)))

\frac{d}{d x} y = (\frac{1}{cos ^{2} ( x )})

limit as x approaches-9 of (8x+72)/(|x+9|)

x \to - 9 lim (\frac{8 x + 72}{∣ x + 9 ∣})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |x-1| ?
The integral from 0 to 3 of |x-1| is 5/2