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

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)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 .

Consider the polynomial f(x)=a x^2+b x+cdot If f(0),f(2)=2, then the minimum value of int_0^2|f^(prime)(x)dxi s___

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

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

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx is

If f(x)="cos"(tan^(-1)x), then the value of the integral int_0^1xf^(x)dx"i s" (3-sqrt(2))/2 (b) (3+sqrt(2))/2 1 (d) 1-3/(2sqrt(2))