phi d phi3.int_(0)^(1)sin^(-1)((2x)/(1+x^(2)))dx

int_(0)^(1)(d)/(dx)["sin"^(-1)(2x)/(1+x^(2))]dx is equal to -

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) and phi(x)=cos^(-1)((1-x^(2))/(1+x^(2))) , then the value of lim_(x to a) (f(x)-f(a))/(phi(x)-phi(a))(0 lt a lt (1)/(2)) is -

According to Leibritz differentiation under the sign of integration can be performed as as below. (i) (d)/(dx)[int_(phi(x))^(Psi(x))f(t)dt]=f{Psi(x)}xx(d)/(dx){Psi(x)}-f{phi(x)}xx(d)/(dx){phi(x)} (ii) (d)/(dx)[int_(phi(x))^(Psi(x))f(x,t)dt]=int_(phi(x))^(Psi(x))(del)/(delx)(f(x,t)dt)+f(x,Psi(x))xx(d)/(dx)Psi(x)-f(x,phi(x))xx(d)/(dx)(phi(x)) The points of maximum of the function f(x)=int_(0)^(x^(2))(t^(2)-5t+4)/(2+e^(t))dt

If phi (x) =int_(1//x)^(sqrt(x)) sin(t^(2))dt then phi ' (1)is equal to

If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int_(0)^(1)f(x)phi(x)dx is

If f(0)=2, f'(x) =f(x), phi (x) = x+f(x) then int_(0)^(1) f(x) phi (x) dx is

If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int_(0)^(1)f(x)phi(x)dx is

The value of int_0^(sin^2theta) sin^-1 sqrt(phi) d phi + int_0^(cos^2theta) cos^-1 sqrt(phi) d phi is equal to (A) pi (B) pi/2 (C) pi/3 (D) pi/4