What is the integral from-3 to 3 of (|x|+|x+1|) ?

The integral from-3 to 3 of (|x|+|x+1|) is 19

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integral from-3 to 3 of (|x|+|x+1|)

\int_{- 3}^{3} (∣ x ∣ + ∣ x + 1 ∣) d x

19

Solution steps

\int_{- 3}^{3} ∣ x ∣ + ∣ x + 1 ∣ d x

Eliminate Absolutes

= \int_{- 3}^{- 1} - x - x - 1 d x + \int_{- 1}^{0} - x + x + 1 d x + \int_{0}^{3} x + x + 1 d x

\int_{- 3}^{- 1} - x - x - 1 d x = 6

\int_{- 1}^{0} - x + x + 1 d x = 1

\int_{0}^{3} x + x + 1 d x = 12

= 6 + 1 + 12

Simplify

= 19

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What is the integral from-3 to 3 of (|x|+|x+1|) ?
The integral from-3 to 3 of (|x|+|x+1|) is 19