sin^(-1)x sqrt(x),0<=x<=1

Differentiate sin^(-1)sqrt(x)(0

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

If y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))) and 0

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))

Differentiate x^x sin^(-1)sqrt(x) where 0 lt x lt 1 w.r.t x

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/2-(sin^(-1)x)/2,""0 < x < 1