[" 11.The value of "int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t)dt],[[" (A) "pi/2," (B) "1," (C) "pi/4," (D) None of these "]]

The value of int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t)dt is

The value of int_(0)^(sin^(2)) sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t)dt , is

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

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

f(x)=int_(0)^(x^(2))((sin^(-1)sqrt(t))^(2))/(sqrt(t))dt

(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.

The value of (int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt) is