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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

Graph

Popular Examples

integral of ln(x)*cos(ln(x))

\int ln (x) \cdot cos (ln (x)) d x

integral of 2/(2x+5)

\int \frac{2}{2 x + 5} d x

integral of ((x^2+7))/(x^2+9)

\int \frac{( x ^{2} + 7 )}{x ^{2} + 9} d x

integral of 1/(sec(3x-1))

\int \frac{1}{sec ( 3 x - 1 )} d x

integral of 1/5 e^{5x-2}

\int \frac{1}{5} e^{5 x - 2} d x

Frequently Asked Questions (FAQ)

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