What is the integral from 1 to 4 of (2-|x-3|) ?

The integral from 1 to 4 of (2-|x-3|) is 7/2

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integral from 1 to 4 of (2-|x-3|)

\int_{1}^{4} (2 - ∣ x - 3 ∣) d x

\frac{7}{2}

Decimal

3.5

Solution steps

\int_{1}^{4} 2 - ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{1}^{3} 2 - (- x + 3) d x + \int_{3}^{4} 2 - (x - 3) d x

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

\int_{3}^{4} 2 - (x - 3) d x = \frac{3}{2}

= 2 + \frac{3}{2}

Simplify

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

= \frac{7}{2}

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What is the integral from 1 to 4 of (2-|x-3|) ?
The integral from 1 to 4 of (2-|x-3|) is 7/2