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Popular Calculus >

integral from 0 to 5 of |x-2|

Solution

\int_{0}^{5} ∣ x - 2 ∣ d x

Solution

\frac{13}{2}

+1

Decimal

6.5

Solution steps

\int_{0}^{5} ∣ x - 2 ∣ d x

Eliminate Absolutes

= \int_{0}^{2} - x + 2 d x + \int_{2}^{5} x - 2 d x

\int_{0}^{2} - x + 2 d x = 2

\int_{2}^{5} x - 2 d x = \frac{9}{2}

= 2 + \frac{9}{2}

Simplify

2 + \frac{9}{2} : \frac{13}{2}

= \frac{13}{2}

Graph

Popular Examples

integral from 0 to 9 of 1/((x-1)^{1/3)}

\int_{0}^{9} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

derivative of axsin(4x+bxcos(4x))

\frac{d}{d x} (a x sin (4 x) + b x cos (4 x))

f^{^{'}} (t) - f (t) = 2 t

limit as x approaches 3+of (-x)/(x-3)

x \to 3 + lim (\frac{- x}{x - 3})

limit as x approaches 8 of 3/((x-8)^2)

x \to 8 lim (\frac{3}{( x - 8 ) ^{2}})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of |x-2| ?
The integral from 0 to 5 of |x-2| is 13/2