If `[x]` denotes the integral part of `x` and `f(x)=min(x-[x],-x-[-x])` show that: `int_-2^2f(x)dx=1`

Let [x] denote the integral part of x in R and g(x)=x-[x]. Let f(x) be any continuous function with f(0)=f(1) then the function h(x)=f(g(x)

Let [x] denote the integral part of x in R and g(x)=x -[x] . Let f(x) be any continous function with f(0) =f(1), then the function h(x) = f(g(x))

If f(x)= |x-21|+|x-1| then evaluate int_-2^2f(x)dx.

Let f(x)=[x] +sqrt({x}) , where [.] denotes the integral part of x and {x} denotes the fractional part of x. Then f^(-1)(x) is

If f is an integrable function, show that int_(-a)^a xf(x^2)dx=0

if f(x)=3x^(2)+4,0<=x<=2 and f(x)=9x-2,2<=x<=4 then show that int_(0)^(4)f(x)dx=66

Let f(x) denote the fractional part of a real number x. Then the value of int_(0)^(sqrt3)f(x^(2))dx is