int_(0)^(sin^(2)x)sin^(-1)(sqrt(t))dt+int_(0)^(oo)cos^(-1)(sqrt(t))dt

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

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

Evaluate the following integrals using properties of integration : int_(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int_(0)^(cos^(2)x)sqrt(t) dt

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))-theta'(x)f(theta(x))

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

Prove that: y=int_(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int_(1/8)^(cos^2x)cos^(-1)sqrt(t) dt , where 0lt=xlt=pi/2 , is the equation of a straight line parallel to the x-axis. Find the equation.

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))