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January 5th, 2017, 04:44 AM   #1
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Minimum integration problem!

How to solve this question?
if f(x)= min{|x-1|, |x-2|,.... |x-n|}
Then what will be the value of integral
INT[f(x)dx] where limit is from 0 to n+1
The options are
1) n+2/4
2) n+3/4
3) n+4/4
4) n+2/2
And Solve it completely if u can!
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January 5th, 2017, 05:09 AM   #2
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Do you understand what "min{|x-1|, |x-2|,.... |x-n|}" means? For example, if 0< x< 1 then -1< x- 1< 0 so 0<|x- 1|< 1 while -2< x- 2< -1 so 1< x- 2< 2, etc. The minimum is |x- 1|. If 1< x< 2, then 0< x- 1< 1 while -1< x- 2< 0 so 0< |x- 2|< 1. |x- 1|= |x- 2| here so the minimum is either one- it doesn't matter which you use. This really only involves basic algebra and arithmetic with a very little Calculus added.
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