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$Evaluate \int_{0}^{100} (x - [x]) d x (where [] re- presents the greatest integer function).$

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Correct option is A

x−[x]={x} has period 1 . Thus, ∫0100 (x−[x])dx=100∫01 {x}dx =100∫01 xdx(∵ for x∈(0,1),(x}=x) =1002x201=50

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Evaluate ∫0100 (x−[x])dx (where [ re- presents the greatest integer function).

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$Evaluate \int_{0}^{100} (x - [x]) d x (where [] re- presents the greatest integer function).$