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Evaluate: ∫ 5 1 { | X − 1 | + | X − 2 | + | X − 3 | } D X . - Mathematics

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Sum

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

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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

Concept: Evaluation of Definite Integrals by Substitution
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