Lot `f(x) =prod_(r=1)^2009 (x-r)`, then the value of the definite integral `int_1^2009 f(x)` is equal to

f(x)=prod_(r=1)^(5)(x+r), then f'(-5) is

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then find the value of the definite integral int_(0)^(1)f(x)dx

int_(0)^( If )(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

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

The value of the definite integral int_(-2008)^(2008)((f'(x)+f'(-x))/((2008)^(x)+1))dx

Let f(x) be a continuous function on [0,4] satisfying f(x)f(4-x)=1. The value of the definite integral int_(0)^(4)(1)/(1+f(x))dx equals -