en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2-|x|

Solution

\int 2 - ∣ x ∣ d x

Solution

2 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 2 - ∣ 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 2 d x - \int ∣ x ∣ d x

\int 2 d x = 2 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 2 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 2 x - \frac{x ∣ x ∣}{2} + C

Popular Examples

tangent of f(x)= 1/x ,(2, 1/2)tangent of

f (x) = \frac{1}{x}, (2, \frac{1}{2})

derivative of (x^3+x^2-2(7+x-x^4))

\frac{d}{d x} ((x^{3} + x^{2} - 2) (7 + x - x^{4}))

integral of ((3(4u+1)^{1/2}))/4

\int \frac{( 3 ( 4 u + 1 ) ^{\frac{1}{2}} )}{4} d u

derivative of 3arccos(x/2)

\frac{d}{d x} (3 arccos (\frac{x}{2}))

integral of (42w^7-7w)/(7w^5)

\int \frac{42 w ^{7} - 7 w}{7 w ^{5}} d w

Frequently Asked Questions (FAQ)

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