Use the residue theorem to evaluate the integral Integral 2pi 0 dq/1 + ecos(q) Solution The denominator of the integrand is 1 + ecosq This becomes 0 when cosq = -1/e q = arc cos (-1/e) q an angle between 0 and 2pi lies inside the contour. Hence residue = limit q tends to arccos(-1/e) of dq = 2pi.