What is the integral of y=|x-1| ?

The integral of y=|x-1| is ((x-1)|x-1|)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of y=|x-1|

integral

y = ∣ x - 1 ∣

\frac{( x - 1 ) ∣ x - 1 ∣}{2} + C

Solution steps

\int ∣ x - 1 ∣ d x

Apply u-substitution

: \int ∣ u ∣ d u

= \int ∣ u ∣ d u

Use the common integral:

\int ∣ u ∣ d u = \frac{u ∣ u ∣}{2}

= \frac{u ∣ u ∣}{2}

Substitute back

u = x - 1

= \frac{( x - 1 ) ∣ x - 1 ∣}{2}

Add a constant to the solution

= \frac{( x - 1 ) ∣ x - 1 ∣}{2} + C

2 x^{2} + 5

\frac{1}{( x ^{2} + 2 x + 8 )}

e^{x} + 1

\frac{x}{1}

\frac{2 ^{3}}{2 \cdot y ^{\frac{1}{2}}}