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Popular Calculus >

integral of 3-|x|

Solution

\int 3 - ∣ x ∣ d x

Solution

3 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 3 - ∣ 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 3 d x - \int ∣ x ∣ d x

\int 3 d x = 3 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 3 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 3 x - \frac{x ∣ x ∣}{2} + C

Graph

Popular Examples

integral of e^{3u}

\int e^{3 u} d u

integral of xe^{-ln(x)}

\int x e^{- l n (x)} d x

integral of sqrt(8-3x)

\int 8 - 3 x d x

integral of x^2e^{2x^3+4}

\int x^{2} e^{2 x^{3} + 4} d x

integral of 10.2+2.5x+0.1x^2

\int 10.2 + 2.5 x + 0.1 x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of 3-|x| ?
The integral of 3-|x| is 3x-(x|x|)/2+C