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Popular Calculus >

integral from-1 to 4 of |x-2|

Solution

\int_{- 1}^{4} ∣ x - 2 ∣ d x

Solution

\frac{13}{2}

+1

Decimal

6.5

Solution steps

\int_{- 1}^{4} ∣ x - 2 ∣ d x

Eliminate Absolutes

= \int_{- 1}^{2} - x + 2 d x + \int_{2}^{4} x - 2 d x

\int_{- 1}^{2} - x + 2 d x = \frac{9}{2}

\int_{2}^{4} x - 2 d x = 2

= \frac{9}{2} + 2

Simplify

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

= \frac{13}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 4 of |x-2| ?
The integral from-1 to 4 of |x-2| is 13/2