Q.2 (15 pts.): Establish the results (2.8) and (2.9) for the integral I = coskn dx, where 71 = xsind _ cx3 COSO. In terms of the following changes of variable; (26) and (2.7) the above integral may be writen to the canonical form (2.8) This is Airy's rainbow integral, first published in his paper entitled "On the Intensity of Light In the neighbourhood of a Caustic" (21]. The significance of the parameter m can be noted by eliminating . from Egs (26) and (2.7) to objain 2ka (tax (29)