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Popular >

integral of 6-|x|

Solution

\int 6 - ∣ x ∣ d x

Solution

6 x - \frac{x ∣ x ∣}{2} + C

Solution steps

\int 6 - ∣ 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 6 d x - \int ∣ x ∣ d x

\int 6 d x = 6 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 6 x - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= 6 x - \frac{x ∣ x ∣}{2} + C

Popular Examples

area y=-x^2+16,y=(-1)/4 x-1,y=x-6.6 area

y = - x^{2} + 16, y = \frac{- 1}{4} x - 1, y = x - 6.6

derivative of y=(7x^2+5)/(x^2+9)derivative of

y = \frac{7 x ^{2} + 5}{x ^{2} + 9}

f(x)=sqrt(xe^x)

f (x) = x e^{x}

integral of 1/(x\sqrt[5]{ln^5(x))}

(dx)/(dt)=4000-x/(50+t)

\frac{d x}{d t} = 4000 - \frac{x}{50 + t}

Frequently Asked Questions (FAQ)

What is the integral of 6-|x| ?
The integral of 6-|x| is 6x-(x|x|)/2+C