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

The integral from-4 to 7 of (|x-2|-3) is -5/2

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integral from-4 to 7 of (|x-2|-3)

\int_{- 4}^{7} (∣ x - 2 ∣ - 3) d x

- \frac{5}{2}

Decimal Notation

- 2.5

Solution steps

\int_{- 4}^{7} ∣ x - 2 ∣ - 3 d x

Eliminate Absolutes

= \int_{- 4}^{2} - x + 2 - 3 d x + \int_{2}^{7} x - 2 - 3 d x

\int_{- 4}^{2} - x + 2 - 3 d x = 0

\int_{2}^{7} x - 2 - 3 d x = - \frac{5}{2}

= 0 - \frac{5}{2}

Simplify

= - \frac{5}{2}

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What is the integral from-4 to 7 of (|x-2|-3) ?
The integral from-4 to 7 of (|x-2|-3) is -5/2