`int_(0)^(15/2)[x-1]dx=` where `[x]` denotes the greatest integer less than or equal to x

The value of the integral, int_1^3 [x^2-2x–2]dx , where [x] denotes the greatest integer less than or equal to x, is :

The value of int_(0)^(2)x^([x^(2)+1])(dx), where [x] is the greatest integer less than or equal to x is

The value of int_(0)^(2) x^([x^(2) +1]) dx , where [x] is the greatest integer less than or equal to x is

The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

The integral I= int_(0)^(2) [x^2] dx ([x] denotes the greatest integer less than or equal to x) is equal to:

If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x where [x] denotes the greatest integer less than or equal to x then

Consider the integral I=int_(0)^(10)([x]e^([x]))/(e^(x-1))dx , where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

The value of the integral int_(-2)^2 sin^2x/(-2[x/pi]+1/2)dx (where [x] denotes the greatest integer less then or equal to x) is