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Question

The value of 55f(x)dx; where f(x)=min({x+1},{x1}),xϵR and {.} denotes fractional part of x is equal to

A
3
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B
4
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C
5
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6
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Solution

The correct option is C 5
55f(x)dx=55(x1[x1])dx

=45(x+5)dx+34(x+4)dx+23(x+3)dx+12(x+1)dx

+01(x)dx+10(x1)dx+21(x2)dx+32(x3)dx

+43(x4)dx+54(x5)dx=5

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