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___`

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

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

Consider the polynomial f(x)=ax^(2)+bx+c. If f(0),f(2)=2 then the minimum value of int_(0)^(2)|f'(x)dx is

If f continuous and differentiable on [0,1] with f(0) = 0 and f(1)=1, then the minimum value of int_0^1(f^(prime)(x))^2dx is

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

Suppose f is continuous on [a,b] & f(a)=f(b)=0 & int_(a)^(b)f^(2)(x)dx=1 then the minimum value of int_(a)^(0)(f^(')(x))^(2)dx int_(a)^(b) x^(2)f^(2)(x)dx is k , then 8k is

What is the value of int_0^pi((f(x))/(f(x)+f(pi/2-x)))dx ?

Let f(x) be a differentiable function in the interval (0,2) , then the value of int_0^2 f(x) dx is :

Consider f(x)=(x^(2))/(2) -kx +1 such that f(0) =0 and f(3)=15 The value of k is