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Popular >

integral of 4-|x|

Solution

\int 4 - ∣ x ∣ d x

Solution

4 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 4 - ∣ 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 4 d x - \int ∣ x ∣ d x

\int 4 d x = 4 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 4 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 4 x - \frac{x ∣ x ∣}{2} + C

Popular Examples

integral from-1 to 1 of sqrt(x+1)-1

\int_{- 1}^{1} x + 1 - 1 d x

integral from-3 to 2 of |x+1|

\int_{- 3}^{2} ∣ x + 1 ∣ d x

limit as x approaches 1 of (2x)/(ln(x))

x \to 1 lim (\frac{2 x}{ln ( x )})

slope of (2.9)(9.7)slope

(2.9) (9.7)

derivative of f(x)=sqrt(6-x)derivative of

f (x) = 6 - x

Frequently Asked Questions (FAQ)

What is the integral of 4-|x| ?
The integral of 4-|x| is 4x-(x|x|)/2+C