int_((-pi)/(4))^(n=-(pi)/(4))|sin x+cos x|dx,n in N=

Evaluate: int_(-(pi)/(4))^(n pi-(pi)/(4))|sin x+cos x|dx

Find value of following definite integrals: int_(-pi/4)^(npi-pi/4)|sin+cosx|dx\ (n in N)

If I_(n) = int_((pi)/(4))^((pi)/(2)) cot^(n) x dx , prove that I_(n) + I_(n-2) = (1)/(n-1)

int_(-(pi)/(4))^((pi)/(4))(2 pi+sin2 pi x)/(2-cos2x)dx

int_(-pi/2)^(pi/2) sin^(m) x. cos^(n) x dx = 0 , if

int_0^(pi/4) (cos x- sin x) dx + int_(pi/4)^((5pi)/4) (sinx-cosx) dx + int_(2pi)^(pi/4) (cosx- sinx) dx =

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

If int_(n)=int_(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then