Tutorial10-sol(1)

# Note in the last integration above the only non zero

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: tion above, the only non-zero contribution comes from the integral of 1/16 as it’s easy to see that 2π 2π cos 2 = cos 4 0 2π 2π cos 2 cos 4 = 0 E =0 0 0 − Evaluate 2− 2 1 cos(4 + 2) + cos(4 − 2) 2 (cos 2 + sin 2 =0 :) ). 2 + 2 =R2 S We apply Green’s Theorem here by noting that 2 2 Q = −2 − − sin 2 + 2 2 2 P = −2 − − cos 2 − 2 2 2 Q − P = 4 − − cos 2 − 2− 2 − 2− 2 cos 2 sin 2 By Green’s Theorem, the integral equals 4 − 2− 2 cos 2 =0 2 + 2 ≤R2 because the integral is anti-symmetric (odd) in in . 3 E and the area of integration is symmetric :) Questions on logical thinking Evaluate the integral − C 2+ 2 , where (a) C is a simple closed piecewise smooth curve not containing the origin in its inside...
View Full Document

## This document was uploaded on 02/10/2014.

Ask a homework question - tutors are online