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Popular Calculus >

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

Solution

\int_{- 3}^{3} 3 - ∣ x ∣ d x

Solution

9

Solution steps

\int_{- 3}^{3} 3 - ∣ x ∣ d x

Eliminate Absolutes

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

\int_{- 3}^{0} 3 - (- x) d x = \frac{9}{2}

\int_{0}^{3} 3 - x d x = \frac{9}{2}

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

Simplify

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

= 9

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-3 to 3 of 3-|x| ?
The integral from-3 to 3 of 3-|x| is 9