If `[x]` denotes the greatest integer less than or equal to `x`, then find the value of the integral `int_(0)^(2)x^(2)[x]dx`.

If [x] denotes the greatest integer less than or equal to x , then find the value of the integral int_0^2x^2[x]dxdot

evaluate the integrals int_(0)^(1)x(1-x)dx

The value of the integral int_-2^(2) |1-x^2|dx is

If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

If [x] denotes the greatest integer less than or equal to x , then evaluate ("lim")_(ntooo)1/(n^2)([1.x]+[2.x]+[3.x]+....+[n.x])

Let [x] denote the greatest integer less than or equal to x . If x = (sqrt(3) +1)^(5) , then [x] is equal to

For a real number y, let [y] denotes the greatest integer less than or equal to y. Then, the function f(x) = (tan pi[(x -pi)])/(1+[2]^(2)) is

Let f (x) = [x] , where [x] denotes the greater integer less than or equal to x. if a = sqrt(2011 ^2 +2012 ) then the value of f (a) is equal to

Evaluate the definite integrals int_(0)^(1)xe^(x^(2))dx