Evaluate: `(int0n[x]dx)/(int0n{x}dx)(w h e r e[x]a n d{x}` are integral and fractional parts of `xa n dn in N)dot`

Evaluate (int_(0)^(n)[x]dx)/(int_(0)^(n){x}dx) (where [x] and {x} are integral and fractional parts of x respectively and n epsilon N ).

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 )

If f(n)=(int_0^n[x]dx)/(int_0^n{x}dx) (where,[*] and {*} denotes greatest integer and fractional part of x and n in N). Then, the value of f(4) is...

Evaluate: int_0^1x(1-x)^n dx

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

Evaluate:- int_0^(pi)[cot x]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate : int x^n log x dx.

Evaluate: int_0^(100)(x-[x]dx(w h e r e[dot] represents the greatest integer function).

Evaluate : int_(0)^(1)x(1-x)^(n)dx

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.