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

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

If f(0)=0, f(3)=3 and f'(3)=4 , then the value of int_(0)^(1)xf'' (3x)dx is equal to

If f(0)=1,f(2)=3,f'(2)=5 and f'(0) is finite,then int_(0)^(1)xf''(2x)dx is equal to (A) zero (B) 1(C)2(D) none of these

A continuous real function f satisfies f(2x)=3(f(x)AA x in R. If int_(0)^(1)f(x)dx=1 then find the value of int_(1)^(2)f(x)dx

If f(0)=1,f(2)=3,f'(2)=5 ,then the value of the definite integral int_(0)^(1)xf''(2x)dx is

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

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

Evaluate: int_(-1)^(4)f(x)dx=4 and int_(2)^(4)(3-f(x))dx=7 then find the value of int_(2)^(-1)f(x)dx

If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0 , then find the value of int_(0)^(a)(dx)/(1+f(x)) .

If f:RrarrR defined by f(x)=sinx+x , then find the value of int_0^pi(f^-1(x))dx