Question 1208838
<pre>

I won't do this for you, but I'll tell you what I would do.

I would use these two definite integrals:

{{{int(cos^0(x),dx,0,pi)}}}{{{""=""}}}{{{int(1,dx,0,pi)}}}{{{""=""}}}{{{x}}}{{{matrix(3,2,"|",pi,"|","","|",0)}}}{{{""=""}}}{{{pi-0}}}{{{""=""}}}{{{pi}}}

{{{int(cos^1(x),dx,0,pi)}}}{{{""=""}}}{{{int(sin(x),dx,0,pi)}}}{{{""=""}}}{{{sin(x)}}}{{{matrix(3,2,"|",pi,"|","","|",0)}}}{{{""=""}}}{{{sin(pi)-sin(0)}}}{{{""=""}}}{{{0-0}}}{{{""=""}}}{{{0}}}

together with this recursion formula from a table of integrals:

{{{int(cos^(n)(x),dx,0,pi)}}}{{{""=""}}}{{{expr(1/n)cos^(n-1)(x)*sin(x)+expr((n-1)/n)*int(cos^(n-2)(x),dx,0,pi)}}}{{{matrix(3,2,"|",pi,"|","","|",0)}}} 

Then find 

{{{int(cos^2(x),dx,0,pi)}}}, {{{int(cos^3(x),dx,0,pi)}}}, {{{int(cos^4(x),dx,0,pi)}}}, etc.,

and see if you can find a pattern to the sequence of integrals, and then what
the integrals are approaching as n approaches infinity,

{{{int(cos^(n)(x),dx,0,pi)}}}

Edwin</pre>