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^(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)^(pi)(t sin t dt)/(sqrt(1+tan^(2)xsin^(2)t)) for 0lt xlt (pi)/2 then

int_(0)^(2 pi)[sin t]dt

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

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

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

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

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

If int_0^x f(t)dt=x+int_x^1 t f(t)dt , then f(1)= (A) 1/2 (B) 0 (C) 1 (D) -1/2

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