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+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(pi/2) is __________

Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(pi/2) 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))a n dg(x) be the inverse of f(x) . Then the value of g'(0)

Let y=f(x) be the solution of the differential equation (dy)/(dx)+k/7 x tan x=1+xtanx-sinx, where f(0)=1 and let k be the minimum value of g(x) where g(x)="max"|(sqrt(193)-1)/2cosy+cos(y+(pi)/3)-x| where yepsilonR then Area bounded by y=f(x) and its inverse between x=(pi)/2 and x=(7pi)/2 is

Let g be the inverse function of a differentiable function f and G (x) =(1)/(g (x)). If f (4) =2 and f '(4) =(1)/(16), then the value of (G'(2))^(2) equals to:

Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x) and g (0)=1 , then intg(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

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