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Popular Calculus >

integral from 0 to 6 of |x-5|

Solution

\int_{0}^{6} ∣ x - 5 ∣ d x

Solution

13

Solution steps

\int_{0}^{6} ∣ x - 5 ∣ d x

Eliminate Absolutes

= \int_{0}^{5} - x + 5 d x + \int_{5}^{6} x - 5 d x

\int_{0}^{5} - x + 5 d x = \frac{25}{2}

\int_{5}^{6} x - 5 d x = \frac{1}{2}

= \frac{25}{2} + \frac{1}{2}

Simplify

\frac{25}{2} + \frac{1}{2} : 13

= 13

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of |x-5| ?
The integral from 0 to 6 of |x-5| is 13