`int_0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx`

By using the properties of definite integrals, evaluate the integrals int0pi/2(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

STATEMENT-1 : int_(-3)^(3)|x|dx=9 STATEMENT-2 : int_(0)^(1)tan^(-1)xdx=(pi)/(4)-lnsqrt(2) STATEMENT-3 : int_(0)^(pi//2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx=(pi)/(4)

Evaluate of each of the following integrals int_(pi//6)^(pi//3)(sqrt("sin"x))/(sqrt(sinx)+sqrt(cosx))"d"x

Evalaute int_(pi//6)^(pi//3)(sqrt((sinx))dx)/(sqrt((sinx))+sqrt((cosx)))

Evalaute int_(pi//6)^(pi//3)(sqrt((sinx))dx)/(sqrt((sinx))+sqrt((cosx)))

int(sinx)/(sqrt(1+sinx))dx

int_0^(pi/2) sqrt(cosx)sinxdx

Comprehension 2 (Q.No 4 to 6) It is known that sqrt(tanx)+sqrt(cotx)={{:(sqrt(sinx)/sqrt(cosx)+sqrt(cosx)/sqrt(sinx), if 0ltxltpi/2),(sqrt(-sinx)/sqrt(cosx)+sqrt(-cosx)/sqrt(-sinx),if pi lt x lt (3pi)/(2)):} d/(dx)(sqrt(tanx)-sqrt(cotx)) =1/2(sqrt(tanx)+sqrt(cotx))(tanx+cotx), AA in (0,pi,2) uu (pi,(3pi)/2) and d/(dx)(sqrt(tanx)+sqrt(cotx))=1/2(sqrt(tanx)-sqrt(cotx))(tanx+cotx), AA x in (0,pi/2) uu (pi, (3pi)/(2)) . Value of the integral I=int(sqrt(tanx)+sqrt(cotx)) dx, where x in (0,pi/2) , is

Differentiate tan^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))} , 0 < x < pi

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=