int_(0)^((pi)/(2))sqrt(1+sin x)dx=

Prove that :int_(0)^((pi)/(2))sqrt(1-sin2x)dx=2(sqrt(2)-1)

Evaluate int_(0)^((pi)/(2))sqrt(1+sin 2x) dx .

int_(0)^((pi)/(4))sqrt(1+sin2x)dx

int_(0)^((pi)/(4)) sqrt(1+sin 2x) dx =

int_(0)^((pi)/(2))(sqrt(sin x))/(sqrt(sin x)+sqrt(cos x))dx

Evaluate : int_(0)^(pi//2) sqrt(1+ sin 2x dx)

Match the following. {:(I,int_(0)^(pi//2)sqrt(1-cos2x)dx=,(a),2),(II,int_(0)^(pi//2)sqrt(1+sin2x)dx=,(b),sqrt2),(III,int_(0)^(1)(x)/(1+x^(2))dx=,(c),log2),(IV,int_(0)^(pi//2)(cosx)/(1+sinx)dx=,(d),(1)/(2)log2):}

int_(0)^(pi//6) sqrt(1-sin 2x) dx

int_(0)^(pi//6) sqrt(1-sin 2x) dx

int_(0)^(pi//2)sqrt(1-sin 2 x dx) is equal to