Let `f(x)=int_0^(sin^2x) sin^-1(sqrt(t))dt+int_0^(cos^2x) cos^-1(sqrt(t))dt`, then (A) `f(x)` is a constant function (B) `f(pi/4)=0` (C) `f(pi/3)=pi/4` (D) `f(pi/4)=pi/4`

If f(x)= int_(0^(sinx) cos^(-1)t dt +int_(0)^(cosx) sin^(-1)t dt, 0 lt x lt (pi)/(2) then f(pi//4) is equal to

If f(x) =int_(0)^(x) {f(t)}^(-1)dt, " and " int_(0)^(1) {f(t}^(-1)dt=sqrt(2) , then f(x)=

If f(x) =int_(0)^(x) sin^(4)t dt , then f(x+2pi) is equal to

Let F(x)=int_(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)] , then

Statement-1: int_(0)^(sin^(2)x) sin^(-1)sqrt(t dt)+int_(0)^(cos^(2)x) cos^(-1)sqrt(t dt)=(pi)/(4) for all x. Statement-2: (d)/(dx) int_(theta(x))overset(psi(x)) f(t)dt=psi'(x)f(psi(x))-psi'(x)f(psi(x))

If f(x)=int_(0)^(cos^(2)x)sec x(sqrt(t))/(1+t^(3))dt then (i) f'(pi)=0( ii) f'(pi)=1 (iii) f'(2 pi)=1( iv )f'(2 pi)=-1

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) pi/(2sqrt(2))

If f(x)=int_(0)^(x)(sin^(4)t+cos^(4)t)dt, then f(x+pi) will be equal to

Let f(x)=int_0^x (sin^100t)/(sin^100t+cos^100t)dt then f(2pi)= (A) 2f(pi/2) (B) 4f(pi/2) (C) f(pi/2) (D) none of these