Exercise Solution 5.4

1. The integral can be solved analytically as

   [s1]

   
2. Consider change of variables x = g(u) defined by

   [s2]

   

   By [2.7], this has Jacobian determinant

   [s3]

   

   With this change of variables, by [2.168], integral [5.42] becomes

   [s4]

   

c,d. See spreadsheet for solutions to parts (c) and (d).