If `f(x)=int_0^(sinx)cos^(- 1)t dt+int_0^(cosx)sin^(- 1)t dt, 0 < x < pi/2,` then `f(pi/4)` is equal to

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^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) none of these

If f(x)=int_0^x{f(t)}^(- 1)dt and int_0^1{f(t)}^(- 1)=sqrt(2), then

If f(x)=int_0^x{f(t)}^(- 1)dt and int_0^1{f(t)}^(- 1)=sqrt(2), then

The value of int_0^(sin^2x)sin^(-1)(sqrtt)dt+int_0^(cos^2x)cos^(-1)(sqrtt)dt is

The value of int _0^(sin^2x)sin^(-1)sqrt(t)dt+int _0^(cos^2x)cos^(-1)sqrt(t)dt is

If f(x)=int_0^x(sint)/t dt ,x >0, then

If f(x)=int_0^x(sint)/t dt ,x >0, then

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.