3

Part of 2007 ISI B.Stat Entrance Exam

Problems(1)

show the following equality involving integration

Source: ISI(BS) 2007 #3

3/8/2012

Let

f(u)

be a continuous function and, for any real number

u

, let denote the greatest integer less than or equal to $u$. Show that for any $x>1$,
\int_{1}^{x} (+1)f(u)du = 2\sum_{i=1}^{[x]} i \int_{i}^{x} f(u)du$$

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