Let `f(x)=min({x},{-x})AA epsilonR`, where {.} denotes the fractional part of `x`. Then `int_(-100)^(100) f(x)dx` is equal to

Options

A. (a) 50
B. (b) 100
C. (c) 200
D. (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`