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

If [x] denotes the integral part of [x] , find int_0^1[x]dx, .

If [x] denotes the integral part of [x] , show that: int_0^((2n-1)pi) [sinx]dx=(1-n)pi,n in N

If [x] denotes the integral part of x and a=int_(-1)^0 (sin^2x)/([x/pi]+1/2)dx, b=int_0^1 (sin^2x)/([x/pi]+1/2)d (x-[x]) , then (A) a=b (B) a=-b (C) a=2b (D) none of these

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) :

If {x} denotes the fractional part of x, then int_(0)^(x)({x}-(1)/(2)) dx is equal to

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

If f is an integrable function such that f(2a-x)=f(x), then prove that int_0^(2a)f(x)dx=2int_0^af(x)dx

If (x) is of the form f(x)=a+b x+c x^2, show that int_0^1f(x)dx=1/6{f(0)+4f(1/2)+f(1)}

If f(x)=1-x+x^(2)-x^(3)+x^(4)+….oo then int_(0)^(x)f(x)dx=

If f is an integrable function, show that int_(-a)^af(x^2)dx=2int_0^af(x^2)dx