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Popular >

integral of |x|-2

Solution

\int ∣ x ∣ - 2 d x

Solution

\frac{x ∣ x ∣}{2} - 2 x + C

Solution steps

\int ∣ x ∣ - 2 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 ∣ x ∣ d x - \int 2 d x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

\int 2 d x = 2 x

= \frac{x ∣ x ∣}{2} - 2 x

Add a constant to the solution

= \frac{x ∣ x ∣}{2} - 2 x + C

Popular Examples

integral of (8sqrt(x)-6)

\int (8 x - 6) d x

integral of xe^{ln(x)}

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

integral of (cot(θ))/(sqrt(sin(θ)))

\int \frac{cot ( θ )}{sin ( θ )} d θ

integral of (5x)/(x^2+6)-1

\int \frac{5 x}{x ^{2} + 6} - 1 d x

integral of (x^2-1)^2(2x)

\int (x^{2} - 1)^{2} (2 x) d x

Frequently Asked Questions (FAQ)

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