`Iff(x)=int_a^x[f(x)]^(-1)dxa n dint_a^1[f(x)]^(-1)dx=sqrt(2),t h e n` `f(2)=2` (b) `f^(prime)(2)=1/2` `f^(prime)(2)=2` (d) `int_0^1f(x)dx=sqrt(2)`

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

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

If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(2))| is___

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Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x)a n df^(prime)(1/4)=0. Then (a) f^(prime)(x) vanishes at least twice on [0,1] (b) f^(prime)(1/2)=0 (c) int_(-1/2)^(1/2)f(x+1/2)sinxdx=0 (d) int_(-1/2)^(1/2)f(t)e^(sinpit)dt=int_(1/2)^1f(1-t)e^(sinpit)dt

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C , then

Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a) f^(prime)(10)=1 (b) f^(prime)(3/2)=-1 (c)domain of f(x) is x geq1 (d)range of f(x)i s(-2,-1)uu(2,oo)