Question

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.

Answer 1

`f(x) ={{:({x}",",, -2le xlt -1), (|"sgn "x|",",,-1le xle1), ({-x}",",, 1lt x le 2):}`
`" "={{:(x+2",",, -2 lex lt -1), (1",",, -1 le x lt 0","), (0",",, x=0),(1",",, 0lt x le 1), (-x+2",",, 1 lt x le 2):}`
The graph fo the function is as shown in the following figure.
`" "` Area `=(2+4)/(2) xx1= 3` sq. units