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Grade:Upto college level

1 Answers

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
10 years ago

Hello majumder

 

Let us assume x = I + f  where I is integral part and f is fractional part ..

intg ( 0 to I ) [x].dx  + intg ( I to I+f) [x].dx

 

I(I-1)/2   + I ( I+f - I)

 

= I(I-1)/2 + I . f    ans

 

Note : Intg ( o to n ) [x] .dx where n is integer = n(n-1)/2 ..so i have used it .

 

Also  intg ( I to I+f) [x] .dx  means x varies from I to I + f ...therefore [x] = I

----= intg ( I to I+f) .I.dx = I ( I+f - I ) = I.f  

 

Is it clear or not !

 

Yagya

askiitians_expert

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