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Let a function f(x) be defined in [-2, 2...

Let a function `f(x)` be defined in `[-2, 2]` as
`f(x) = {{:({x}",",, -2 le xlt -1), (|"sgn "x|",",,-1le x le 1),({-x}",",, 1 lt xle 2):}` where `{x}` and sgn `x` denote fractional part and signum functions, respectively. Then find the area bounded by the graph of `f(x)` an the x-axis.

A

2 sq. units

B

3 sq. units

C

4 sq. units

D

5 sq. units

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)={{:({x}",",-2lexlt-1),(|sgnx|",",-1lexle1),({-x}",",1ltxle2):}`
The graph of f(x) is

Area `=(2+4)/(2)xx1=3` sq. units
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