What is the integral from-2 to 5 of (3+x-2|x|) ?

The integral from-2 to 5 of (3+x-2|x|) is 5/2

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integral from-2 to 5 of (3+x-2|x|)

\int_{- 2}^{5} (3 + x - 2 ∣ x ∣) d x

\frac{5}{2}

Decimal

2.5

Solution steps

\int_{- 2}^{5} 3 + x - 2 ∣ x ∣ d x

Eliminate Absolutes

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

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

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

= 0 + \frac{5}{2}

Simplify

= \frac{5}{2}

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What is the integral from-2 to 5 of (3+x-2|x|) ?
The integral from-2 to 5 of (3+x-2|x|) is 5/2