Consider the function f(x)= _ 0 ^ x [t] d t where x>0 and is the integral part of . Then
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Consider the function \(f(x)=\int_{0}^{x}[t] d t\)
where \(x>0\) and
is the integral part of 
. Then
where \(x>0\) and
is the integral part of . Then
is not defined for \(x=1,2,3, \ldots\)
is defined for all \(x>0\) but is not continuous at
\(x=1,2,3, \ldots\)
is continuous for all \(x>0\)
is differentiable for all \(x>0\)
Answer
(C) is continuous for all x>0
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