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Popular >

integral of 1-|x|

Solution

\int 1 - ∣ x ∣ d 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

Popular Examples

integral of (x^2-cos(x))

\int (x^{2} - cos (x)) d x

integral of 4sec^2(4x-2)

\int 4 sec^{2} (4 x - 2) d x

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

\int (\frac{2}{x} + \frac{x}{3})^{2} d x

integral of (3x^2+5cos(x)+2)

\int (3 x^{2} + 5 cos (x) + 2) d x

integral of 10cos(x)

\int 10 cos (x) d x

Frequently Asked Questions (FAQ)

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