∫−3/210 {2x}dx where {.} denotes the fractional part of  x, is equal to

f(x)={2x} is a periodic function with period  12LetI=∫−3/210 {2x}dx=∫−3(1/2)20(1/2) {2x}dx=23∫01/2 2xdx as {2x}=2x−[2x] and when ∈0,12,[2x]=0=23x201/2=234