en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 5-|x|

Solution

\int 5 - ∣ x ∣ d x

Solution

5 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 5 - ∣ 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 5 d x - \int ∣ x ∣ d x

\int 5 d x = 5 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 5 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 5 x - \frac{x ∣ x ∣}{2} + C

Graph

Popular Examples

integral of t/(e^{-t)}

integral of 4sin(x)+5sinh(x)

integral of 8/3 cos^3(x)

integral of 1/((5x+11)^2)

integral of (3000)/(sqrt(400x))

Frequently Asked Questions (FAQ)

What is the integral of 5-|x| ?
The integral of 5-|x| is 5x-(x|x|)/2+C