Evaluation of definite integrals

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Question

$Let f (x) = maximum {x + | x |, x - [x]}, where [x] is the greatest integer less than or equal to$ $x. Then \int_{- 2}^{2} f (x) d x =$

Moderate

Solution

$\begin{array}{l} \int_{- 2}^{2} f (x) d x = \int_{- 2}^{0} {x} d x + \int_{0}^{2} 2 x d x \\ = (2 \times \frac{1}{2} \times 1 \times 1) + (4 - 0) \\ = 1 + 4 = 5 \end{array}$

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