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Popular Calculus >

integral from-3 to 3 of (6-|x|)

Solution

\int_{- 3}^{3} (6 - ∣ x ∣) d x

Solution

27

Solution steps

\int_{- 3}^{3} 6 - ∣ x ∣ d x

Eliminate Absolutes

= \int_{- 3}^{0} 6 - (- x) d x + \int_{0}^{3} 6 - x d x

\int_{- 3}^{0} 6 - (- x) d x = \frac{27}{2}

\int_{0}^{3} 6 - x d x = \frac{27}{2}

= \frac{27}{2} + \frac{27}{2}

Simplify

\frac{27}{2} + \frac{27}{2} : 27

= 27

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-3 to 3 of (6-|x|) ?
The integral from-3 to 3 of (6-|x|) is 27