Show that `int_0^(p+qpi)|cosx|dx=2q+sin p` where `q in N & -pi/2 < p< pi/2.`

Show that int_(0)^(p+q pi)|cos x|dx=2q+sin p where q in N&-(pi)/(2)

Show that int_(0)^(2pi) g(cosx)dx=2int_(0)^pi g(cosx)dx , wher g(cosx) is a function of cosx .

What is int_0^(pi//2) |sin x-cosx|dx equal to

Show that int_(0)^(pi) g (sinx)dx=2 int_(0)^((pi)/(2))g(sin)dx , where g(sinx) is a function of sinx .

Show that (a) int_(0)^(pi/2) sin x dx=1 (b) int_(0)^(pi) cosx dx=0

IfI_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)d ,a n dI_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.

IfI_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)d ,a n dI_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .