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Question
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
Solution
= `int_1^5 {| x - 1| + | x - 2| + |x - 3|} dx`
= `int_1^5 (x - 1)dx + int_1^2 (2 - x)dx + int_2^5 (x - 2) dx + int_1^3 (3 - x) dx + int_3^5 ( x - 3) dx`
= `[x^2/2 - x]_1^5 + [2x - x^2/2]_1^2 + [x^2/2 - 2x]_2^5 + [3x - x^2/2]_1^3 + [x^2/3 - 3x]_3^5`
= 17
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