Let `I_m=int_0^pi (1-cosmx)/(1-cosx)dx`. Show that `I_m=mpi`.

int_0^(pi/2) cosx/(1+sinx)dx

Let I_(m)=int_(0)^(pi)((1-cos mx)/(1-cos x))dx use mathematical induction to prove that l_(m)= m pi, m=0,1,2 ......

int_0^pi sqrt(1+cosx)/(1-cosx)^(5//2) dx

int_(0)^(pi)(cos x)/(1-sin^(m)x)dx

solve int_0^pi (x sinx)/(1+cosx) dx=

int_0^(pi/2) cosx/sqrt(1+sinx)dx

If I_n= int_0^pi (1-cos2nx)/(1-cos2x)dx or int_0^pi (sin^2nx)/(sin^2x) dx, show that I_1, I_2, I_3…………. are inA.P.

int_0^(pi/2) (Cosx - Sinx)dx

Evaluate int_0^(pi/2)cosx/(1+cosx+sinx)dx