This preview shows page 1. Sign up to view the full content.
Unformatted text preview: / 2. 2. (30 pts.) Evaluate the following integrals using contour integration: (a) (10 pts.) i dx (1 + x 2 ) 2 , (b) (20 pts.) i dx 1 + x 3 . [Hint for (b): use the boundary of a 120 circular sector of large radius as integration contour] 3. (30 pts.) Show that (a) (15 pts.) i (ln x ) 2 1 + x 2 dx = 3 8 , (b) (15 pts.) i ln x 1 + x 2 dx = 0 . [Hint: Obtain both integrals simultaneously by integrating some branch of (log z ) 2 / (1 + z 2 ) around a large semicircle indented at z = 0.] 4. (20 pts.) Evaluate i x 1 + x 4 dx for real. What are the restrictions on real for this integral to exist? Due at 5pm on Wed. November 25....
View
Full
Document
 Fall '09
 PROF

Click to edit the document details