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

int_0^pi dx/(1+cosx)

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 ......

Find I=int_0^pi ln(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.

Evaluate: int_0^pi log(1+cosx)dx

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

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

Evaluate: int_0^pilog(1+cosx)dx