If `F(x)=int(((1+x)[(1-x+x^(2))(1+x+x^(2))+x^(2)]))/((1+2x+3x^(2)+4x^(3)+3x^(4)+2x^(5)+x^(6)))dx` then find the value of `[F(99)-F(3)]`.Note: `[k]` denotes greatest integer less than or equal to `k`

The value of int_(1)^(3) (|x-2|+[x])dx is ([x] stands for greatest integer less than or equal to x)

If x^(2)+3x+5 is the greatest common divisor of (x^(3)+ax^(2)+bx+1) and (2x^(3)+7x^(2)+13x+5) then find the value of [a+b]. [Note : [k] denotes greatest integer less than or equal to k.]

int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3)+2x^(2)+5)dx=F(x) Fidn the value of [F(1)-F(0)] where [.] represents greatest integer function

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 :

let f:R rarr R be given by f(x)=[x]^(2)+[x+1]-3, where [x] denotes the greatest integer less than or equal to x. Then,f(x) is

If f(x)={x}+{x+[(x)/(1+x^(2))]}+{x+[(x)/(1+2x^(2))]}+{x+[(x)/(1+3x^(2))]}.......+{x+[(x)/(1+99x^(2))]} , then values of [f(sqrt(3))] is where [*] denotes greatest integer function and {*} represent fractional part function)

Let f(x)=x-x^(2) and g(x)=ax . If the area bounded by f(x) and g(x) is equal to the area bounded by the curves x=3y-y^(2) and x+y=3 , then find the value of |[a]| : [Note: denotes the greatest integer less than or equal to k.]