`[sin n-cos x]_(0)^( pi/4)`

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

If A(x)=det[[x^(n),sin x,cos xn!sin((n pi)/(2)),cos((n pi)/(2))a,a^(2),a^(3)]], then the value of (d^(n))/(dx^(n))[Delta(x)] at x=0 is

Q.the value of the integral int_(0)^((pi)/(4))(cos^(2)x)/(sin x+cos x)+int_((pi)/(4))^(0)(sin^(2))/(sin x+cos x)

Evaluate :int_(0)^((pi)/(2))(a sin x+b cos x)/(sin((pi)/(4)+x))dx

If f(x)=sqrt(1-sin2x), then f'(x) is equal to -(cos x+sin x), for x in((pi)/(4),(pi)/(2))cos x+sin x, for x in(0,(pi)/(4))-(cos x+sin x), for x in(0,(pi)/(4))cos x-sin x, for x in((pi)/(4),(pi)/(2))

Evaluate the following : int_(0)^(pi//4)(sin 2x)/(sin^(4)x+cos^(4)x)dx.

Evaluate the definite integrals int_(0)^((pi)/(4))(sin x cos x)/(cos^(4)x+sin^(2)x)dx

int_(0)^(x)|sin t|dt, where x in(2n pi,(2n+1)pi)n in N, is equal to (A)4n-cos x(B)4n-sin x(C)4n+1-cos x(D)4n-1-cos x

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