" 11."sin^(-1)sqrt((1-x)/(1+x))

(iv) If y=tan^(-1)(x/(1+sqrt(1-x^(2))))+sin(2tan^(-1)sqrt((1-x)/(1+x))) , then find (dy)/(dx) for x epsilon(-1,1)

sin^(-1)x+sin^(-1)sqrt(1-x^(2))

intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(1-x)))+p , then p is equal to 0 (b) 1/(sqrt(1-x)) sin^(-1)sqrt(x) (d) 1/(sqrt(1-x^2))

The solution set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x=(cot^(-1)(sqrt(1-x^(2))))/(x)-sin^(-1)x is (a) [-1,1]-{0}(b)(0,1)uu{-1}(c)(-1,0)uu{1} (d) [-1,1]

int sqrt((x)/(1-x))dx is equal to sin^(-1)sqrt(x)+C(b)sin^(-1){sqrt(x)-sqrt(x(1-x))}+C(c)sin^(-1){sqrt(x(1-x)}+C(d))sin^(-1)sqrt(x)-sqrt(x(1-x))+C

If sin^(-1)x+sin^(-1)(1-x)=sin^(-1)sqrt(1-x^(2)), then x is equal to

Differentiate w.r.t.x the function in Exercises 1 to 11. sin^(-1)(x sqrt(x)), 0 le x le 1 .

Differentiate w.r.t.x the function in Exercises 1 to 11. sin^(-1)(x sqrt(x)), 0 le x le 1 .