What is the integral from-2 to 3 of (2-|x-1|) ?

The integral from-2 to 3 of (2-|x-1|) is 7/2

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integral from-2 to 3 of (2-|x-1|)

\int_{- 2}^{3} (2 - ∣ x - 1 ∣) d x

\frac{7}{2}

Decimal

3.5

Solution steps

\int_{- 2}^{3} 2 - ∣ x - 1 ∣ d x

Eliminate Absolutes

= \int_{- 2}^{1} 2 - (- x + 1) d x + \int_{1}^{3} 2 - (x - 1) d x

\int_{- 2}^{1} 2 - (- x + 1) d x = \frac{3}{2}

\int_{1}^{3} 2 - (x - 1) d x = 2

= \frac{3}{2} + 2

Simplify

\frac{3}{2} + 2 : \frac{7}{2}

= \frac{7}{2}

What is the integral from-2 to 3 of (2-|x-1|) ?
The integral from-2 to 3 of (2-|x-1|) is 7/2