What is the integral from 3 to 7 of (|x-4|-|x-5|) ?

The integral from 3 to 7 of (|x-4|-|x-5|) is 1

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integral from 3 to 7 of (|x-4|-|x-5|)

\int_{3}^{7} (∣ x - 4 ∣ - ∣ x - 5 ∣) d x

1

Solution steps

\int_{3}^{7} ∣ x - 4 ∣ - ∣ x - 5 ∣ d x

Eliminate Absolutes

= \int_{3}^{4} - x + 4 - (- x + 5) d x + \int_{4}^{5} x - 4 - (- x + 5) d x + \int_{5}^{7} x - 4 - (x - 5) d x

\int_{3}^{4} - x + 4 - (- x + 5) d x = - 1

\int_{4}^{5} x - 4 - (- x + 5) d x = 0

\int_{5}^{7} x - 4 - (x - 5) d x = 2

= - 1 + 0 + 2

Simplify

= 1

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\int_{0}^{4} π (x)^{2} d x

What is the integral from 3 to 7 of (|x-4|-|x-5|) ?
The integral from 3 to 7 of (|x-4|-|x-5|) is 1