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

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

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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

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