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Popular Calculus >

integral of 2-|x|

Solution

\int 2 - ∣ x ∣ d x

Solution

2 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 2 - ∣ x ∣ 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 d x - \int ∣ x ∣ d x

\int 2 d x = 2 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 2 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 2 x - \frac{x ∣ x ∣}{2} + C

Graph

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Frequently Asked Questions (FAQ)

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