Let `f:[0,2] in R` be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1. Let `F(x)=int_(0)^(x^(2)) f(sqrt(t))dt` for `x in [0,2]`If F'(x)=f'(x) for all `x in (0,2), then F(2) equals

Let f:[0,2]to RR be a function which is continuous on [0,2] and is differentiable on (0, 2) with f(0)=1 . Let F(x)=int_(0)^(x^(2))f(sqrt(t))dt" for "x in[0,2] . If F'(x)=f'(x) for all x in(0,2) , the F(2) equals

Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and is differentiable on (0 , 2) with f(0) = 1. Let F(x) = int_0^(x^2) f(sqrtt)dt for x in [0,2] . If F'(x) = f'(x) for all x in (0,2) , then F(2) equals

Let f : [0, 2]to R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0)=1 . Let F(x)=int_(0)^(x^(2))f(sqrt(t))dt , for x in [0, 2] . If F'(x)=f'(x), AA x in (0, 2) , then F (2) equals :

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a) e^2-1 (b) e^4-1 (c) e-1 (d) e^4

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a)e^2-1 (b) e^4-1 (c)e-1 (d) e^4

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a) e^2-1 (b) e^4-1 (c) e-1 (d) e^4

Let f:[0,2]vecR be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dt for x in [0,2] . If F^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals

If f(x) is continuous on [0,2] , differentiable in (0,2) ,f(0)=2, f(2)=8 and f'(x) le 3 for all x in (0,2) , then find the value of f(1) .