What is the integral from 2 to 5 of (3-|x-4|) ?

The integral from 2 to 5 of (3-|x-4|) is 13/2

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integral from 2 to 5 of (3-|x-4|)

\int_{2}^{5} (3 - ∣ x - 4 ∣) d x

\frac{13}{2}

Decimal Notation

6.5

Solution steps

\int_{2}^{5} 3 - ∣ x - 4 ∣ d x

Eliminate Absolutes

= \int_{2}^{4} 3 - (- x + 4) d x + \int_{4}^{5} 3 - (x - 4) d x

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

\int_{4}^{5} 3 - (x - 4) d x = \frac{5}{2}

= 4 + \frac{5}{2}

Simplify

4 + \frac{5}{2} : \frac{13}{2}

= \frac{13}{2}

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\int_{0}^{b} e^{- s \cdot t} \cdot t d t

\int_{e}^{4} \frac{1}{4 x} d x

What is the integral from 2 to 5 of (3-|x-4|) ?
The integral from 2 to 5 of (3-|x-4|) is 13/2