`int_0^n x-[x] dx`

int_0^3 [x] dx

If n in N , the value of int_(0)^(n) [x] dx (where [x] is the greatest integer function) is

For any n in R^(+) , the value of the integral int_(0)^(n[x]) (x-[x])dx is

LetI_(1)=int_(0)^(n)[x]dx and I_(2)=int_(0)^(n){x}dx where [x] and {x} are integral and fractionalparts of x and n in N-{1}. Then (I_(1))/(I_(2)) is equal to

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 ).

What is int_0^1 x(1-x)^n dx equal to

The value of the integral int_0^1 x(1-x)^n dx=