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Please find attached the image of the problem The problem is a sub problem of a problem. The integral value is 0 as per my knowledge but this does not give all the values of x . The answer given in book is [x]*{x} which satisfies all the values of x. Where [x] = greatest integer function ;{x} = fractional part

Please find attached the image of the problem
The problem is a sub problem of a problem.
 
The integral value is 0 as per my knowledge but this does not give all the values of x .
 
The answer given in book is [x]*{x} which satisfies all the values of x. Where [x] = greatest integer function ;{x} = fractional part

Question Image
Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
2 years ago
first of all the ques in the book is wrong coz the variable of integration and the variable in limits cant be the same.
correct ques should be 
∫ [t] dt from 0 to {x}
now, this means that t ranges from 0 to {x}.
but {x} is less than 1 so that t lies in 0 to 1.
where [t] = 0
so, integral does in fact equal 0 (zero).
kindly approve :))

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