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Popular Calculus >

integral of 1-|x|

Solution

integral

1 - ∣ x ∣

Solution

x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 1 - ∣ 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 1 d x - \int ∣ x ∣ d x

\int 1 d x = x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= x - \frac{x ∣ x ∣}{2} + C

Graph

Popular Examples

integral of (1-x)^3

integral of e^2x^2

integral of 1/((2x+1)^3)

integral of (cos(1/x))/(x^3)

integral of 1/(1+cos^2(x))

Frequently Asked Questions (FAQ)

What is the integral of 1-|x| ?
The integral of 1-|x| is x-(x|x|)/2+C