" 11."pi(x)=sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))" à "

(d)/(dx)[sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))] is

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

Find (dy)/(dx), if y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]

The value of sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))] is equal to

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))

sin^(-1)sqrt(x)+sin^(-1)sqrt(1-x)=(pi)/(2)

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

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

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x =1/(sqrt(2))ltxle1

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x,-1/(sqrt(2))ltxle1