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).