If `f(x) = min({x}, {-x}) x in R`, where {x} denotes the fractional part of x, then `int_(-100)^(100)f(x)dx` is

Options

A. 50
B. 100
C. 200
D. none of these

Answer

A

Explanation

The graph with solid line is the graph of `f(x)={x}` and the graph with dotted lines is the graph of `f(x)={-x}`. Now, the graph of min `({x},{-x})` is the graph with dark solid lines.
`int_(-100)^(100) f(x)dx=` Area of 200 triangles shown as solid dark lines in the diagram
`=2001/2(1)=50`