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Popular Calculus >

integral from 0 to 8 of (5-|x-3|)

Solution

\int_{0}^{8} (5 - ∣ x - 3 ∣) d x

Solution

23

Solution steps

\int_{0}^{8} 5 - ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{0}^{3} 5 - (- x + 3) d x + \int_{3}^{8} 5 - (x - 3) d x

\int_{0}^{3} 5 - (- x + 3) d x = \frac{21}{2}

\int_{3}^{8} 5 - (x - 3) d x = \frac{25}{2}

= \frac{21}{2} + \frac{25}{2}

Simplify

\frac{21}{2} + \frac{25}{2} : 23

= 23

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 8 of (5-|x-3|) ?
The integral from 0 to 8 of (5-|x-3|) is 23