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

int_(0)^(pi/2)sqrt(1-sin2x)dx is equal to

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):}

Evaluate: int_(0)^( pi/4)sqrt(1+sin2x)dx (ii) int_(0)^( pi/4)sqrt(1-sin2x)dx

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

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

int_(0)^( pi//2)sqrt((1-sin2x)/(1+sin2x))dx

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

Evaluate : int_(0)^(pi)sqrt(1+sin2x)dx .

Prove that : int_0^(pi/2)sqrt(1-sin2x)dx=2(sqrt(2)-1)

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