Evaluate: `int_0^2 ([x]+|x-1|)dx` (where [.] represents G.I.F.).

Evaluate: int_0^1(3x^2+5x)dx

Evaluate: int_0^(100)x-[x]dx where [dot] represents the greatest integer function).

The value of int_0^(2pi)[2 sin x] dx , where [.] represents the greatest integral functions, is

The function f(x)=x^2e^(-2x),x > 0. If l is maximum value of f(x) find [l^(-1)] (where [ ] denotes G.I.F.).

Evaluate: int_0^(1)x(dx)/(sqrt(1-x^(2)))

Evaluate the integral I=int_(0)^(2)|x-1|dx .

The value of int_(-2)^2 (sin^2x)/([x/pi]+1/2) dx is where [*] =G.I.F (A) 1 (B) 0 (C) 2 (D) -1

Evaluate: int[f(x)g''(x)-f''(x)g(x)]dx

If f(x)=int(2+sqrt(x))/((x+1+sqrt(x))^2)dx and f(0)=0 then the value of If [f(4)] is: (where [.] represents the greatest integer function) .

Evaluate : (i) int_(-1)^(2){2x}dx (where function {*} denotes fractional part function) (ii) int_(0)^(10x)(|sinx|+|cosx|) dx (iii) (int_(0)^(n)[x]dx)/(int_(0)^(n)[x]dx) where [x] and {x} are integral and fractional parts of the x and n in N (iv) int_(0)^(210)(|sinx|-[|(sinx)/(2)|])dx (where [] denotes the greatest integer function and n in 1 )