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NDA Math Definite Integrals

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For th next two (2) items that follow :
Consider the function
f(x)=xg(x) and g(x)=

1

[x]

Where [⋅] is the greatest integer function

[NDA I 2016]

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Question : 36

Total: 62

What is ∫

1f(x)dx equal to ?

37
72
2
3
17
72
37
144

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