Let `g(x)` be differentiable on `R` and `int_(sint)^1x^2g(x)dx=(1-sint),` where `t in (0,pi/2)dot` Then the value of `g(1/(sqrt(2)))` is____

If g(x) is a differentiable function such that int_(1)^(sinalpha)x^(2)g(x)dx=(sin alpha-1), AA alpha in (0,(pi)/(2)) , then the value of g((1)/(3)) is equal to

Let g(x)=int(1+2cos x)/((cos x+2)^(2))dx and g(0)=0. then the value of 8g((pi)/(2)) is

Let f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4))) and g be the inverse of f then the value of g^(')(0) is

Let f(x)=x^(3)+x-2 be a function than int_(-2)^(0)g(x)dx equals where g(x)=f^(-1)x

Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x) and g (0)=1 , then g(x)((2-sin2x)/(1-cos2x))dx is equal to

Let f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4)) and g be the inverse of f. Then , the value of g'(0) is

Let f(x)=int_(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x) . Then the value of 4 (g''(x))/(g(x)^(2)) is________.

Let f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4))) and g be the inverse of f. Then,the value of g'(x) is

int_0^1 (tan^-1x)/xdx-1/2int_0^(pi/2) t/sint dt has the value (A) -1 (B) 1 (C) 2 (D) 0