`Ifint_0^(f(x))t^2dt=xcospix ,t h e nf^(prime)(9)i s` `-1/9` (b) `-1/3` (c) `1/3` (d) non-existent

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If int_(sinx)^1 t^2f(t)dt=1-sinx , then the value of f(1/sqrt(3)) is (A) 1/sqrt(3) (B) 1/3 (C) sqrt(3) (D) 3

If int_0^x f(t)dt=x+int_x^1 t f(t)dt , then f(1)= (A) 1/2 (B) 0 (C) 1 (D) -1/2

If F(t)=int(x+y)dt then the value of F(pi/2)-F(0) is 1 (b) -1 (c) e^(pi//2) (d) 0

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is

If int_(0)^(1)(e^(t))/(t+1)dt=a, then int_(b-1)^(b)(e^(-t))/(t-b-1)dt=

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

If f(1)=3,f^(prime)(1)=2,f^(1)=4,t h e n(f^(-1))^()(3)= a. 1 b. -1/2 c. -2 d. none of these