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Popular Calculus >

integral from-1 to 3 of |x-2|

Solution

\int_{- 1}^{3} ∣ x - 2 ∣ d x

Solution

5

Solution steps

\int_{- 1}^{3} ∣ x - 2 ∣ d x

Eliminate Absolutes

= \int_{- 1}^{2} - x + 2 d x + \int_{2}^{3} x - 2 d x

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

\int_{2}^{3} x - 2 d x = \frac{1}{2}

= \frac{9}{2} + \frac{1}{2}

Simplify

\frac{9}{2} + \frac{1}{2} : 5

= 5

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of |x-2| ?
The integral from-1 to 3 of |x-2| is 5