GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 16 of 65

Marks: +1, -0

Let

{f}

be a real valued function of a real variable defined as

f(x)=x-[x]

, where

[x]

denotes the largest integer less than or equal to

x

. The value of

∫↙{0.25}↖{1.25} f(x) d x

is _____________ (up to 2 decimal places).

Solution:

f(x)=x-[x]=\{x\}=

fractional part of

x

Graph of fractional part of

x

is given below.

It is periodic with period 1.

∫↙{0.25}↖{1.25} f(x) d x=∫↙{0}↖{1} f(x) d x=\;{1}/{2} × 1 × 1=0.5

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