Exercise Solution 5.3

1. The integral is solved analytically as

   [s1]

   
2. Given change of variables

   [s2]

   

   the inverse is

   [s3]

   

   so the new bounds of integration are g^–1(1) = 1 and g^–1(–1) = 0. By [2.166], change of variables [s2] converts integral [5.40] to

   [s4]

   

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