What is the integral from (-2) to 8 of (|x-2|-3) ?

The integral from (-2) to 8 of (|x-2|-3) is -4

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integral from (-2) to 8 of (|x-2|-3)

\int_{(- 2)}^{8} (∣ x - 2 ∣ - 3) d x

- 4

Solution steps

\int_{(- 2)}^{8} ∣ x - 2 ∣ - 3 d x

Eliminate Absolutes

= \int_{(- 2)}^{2} - x + 2 - 3 d x + \int_{2}^{8} x - 2 - 3 d x

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

\int_{2}^{8} x - 2 - 3 d x = 0

= - 4 + 0

Simplify

= - 4

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What is the integral from (-2) to 8 of (|x-2|-3) ?
The integral from (-2) to 8 of (|x-2|-3) is -4