" I."quad sin^(-1)(x sqrt(x));quad 0<=x<=1

int_0^1 sin^-1x/sqrt(1+x)dx

Evaluate int (1)/(sqrt( sin^(-1)x) sqrt(1-x^(2))) dx " on " I=(0,1)

If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in (0, 1/2) , then f'(x) has the value equal to (i) 2/(xsqrt(1-x)) (ii) 0 (iii) -2/(xsqrt(1-x)) (iv) pi

If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in (0, 1/2) , then f'(x) has the value equal to (i) 2/(xsqrt(1-x)) (ii) 0 (iii) -2/(xsqrt(1-x)) (iv) pi

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

Evaluate int (1)/(sqrt(sin ^(-1) x sqrt(1-x^(2))))dx on I= (0,1).

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

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

Let I=int_(0)^(1) (sin x)/(sqrt(x))dx and I=int_(0)^(1) (cos x)/(sqrt(x))int dx . Then, which one of the following is true?