`(dy)/(dx)a tx=(sqrt(pi))/2ify=sqrt(sin^4x^2+cos^4x^2)`

Find (dy)/(dx) if y = log (sqrt(2x + sqrt(4x^2 + a^2)))

Evaluate : int_0^(pi/2) sqrt(sin^4 x)/sqrt(sin^4 x) + sqrt(cos^4 x) dx

Ify,=sqrt(((1+cos x)/(2))), provethat (dy)/(dx)=-(1)/(2)(sin x)/(2) If y,=sqrt((1+sin x)/(1-sin x)), prove that cos x(dy)/(dx)=y

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

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Find the derivatives of the following functions at the indicated points. sqrt(sin^4x^2 +cos^4x^2) at x = (sqrt(pi/2))

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