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

Let f(x)=e^(x)+2x+1 then find the value of int_(2)^(e+3)f^(-1)(x)dx

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:RrarrR defined by f(x)=sinx+x , then find the value of int_0^pi(f^-1(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 a continuous function f on [0,a] satis fies f(x)f(a-x)=1,a>0 then find the value of int_(0)^(a)(dx)/(1+f(x))

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 continous function on R. If int_(0)^(1)[f(x)-f(2x)]dx=5 and int_(0)^(2)[f(x)-f(4x)]dx=10 then the value of int_(0)^(1)[f(x)-f(8x)]dx=

[" Let "f" be a twice differential function "],[" satisfying "(e^(x)f''(x)-e^(x)f'(x))/(e^(2x))=1" and "],[f(0)=0,f'(0)=1," then the value of "],[int_(0)^(1)(f(x))/(x)dx" is "]