What is the integral of |x-2| ?

The integral of |x-2| is ((x-2)|x-2|)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of |x-2|

\int ∣ x - 2 ∣ d x

\frac{( x - 2 ) ∣ x - 2 ∣}{2} + C

Solution steps

\int ∣ x - 2 ∣ d x

Apply u-substitution

= \int ∣ u ∣ d u

Use the common integral:

\int ∣ u ∣ d u = \frac{u ∣ u ∣}{2}

= \frac{u ∣ u ∣}{2}

Substitute back

u = x - 2

= \frac{( x - 2 ) ∣ x - 2 ∣}{2}

Add a constant to the solution

= \frac{( x - 2 ) ∣ x - 2 ∣}{2} + C

t an g e n t x^{4} + 7 e^{x}

n = 0 \sum \infty 9 (\frac{5}{12})^{n}

\frac{d}{d x} ((x^{2} + 1)^{\frac{1}{2}})

a re a y = sin (x), y = cos (x), x = \frac{5 π}{4}, x = 2 π

t an g e n t y = \frac{2 x}{x + 2}, (2, 1)