If `f(x)={0` ,where `x=n/(n+1),n=1,2,3.... and 1` else where then the value of `int_0^2 f(x) dx` is

A function f is defined by f(x)=1/(2^(r-1)),1/(2^r)ltxlt=1 (2^(r-1)),r="1,2,3 then the value of int_0^1f(x)dx

If f(0)=1,f(2)=3,f^'(2)=5 ,then find the value of int_0^1xf^('')(2x)dx

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

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

"If " f(x)=int(dx)/(x^(1//3)+2) " and "f(0)=12log_(e)2, " then the value of " f(-1) " is"-.

Let (5 + 2sqrt6)^n= p+ f , where n in N and p in N and 0

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

If a_0 = x,a_(n+1)= f(a_n) , where n = 0, 1, 2, ..., then answer thefollowing questions. If f (x) = msqrt(a-x^m),x lt0,m leq 2,m in N ,then

If int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1 , then the value of the integral int_-1^1(f(x))dx is equal to