Math 104: Improper Integrals (With Solutions)
                                                         Ryan Blair
                                                 University of Pennsylvania
                                             Tuesday March 12, 2013
            Ryan Blair (U Penn)                    Math 104: Improper Integrals               Tuesday March 12, 2013      1 / 15
    Outline
     1   Improper Integrals
            Ryan Blair (U Penn)                    Math 104: Improper Integrals               Tuesday March 12, 2013      2 / 15
                                              Improper Integrals
    Improper integrals
    Definite integrals Z b f (x)dx were required to have
                                      a
            finite domain of integration [a;b]
            finite integrand f (x) < ±∞
            Ryan Blair (U Penn)                    Math 104: Improper Integrals               Tuesday March 12, 2013      3 / 15
                                              Improper Integrals
    Improper integrals
    Definite integrals Z b f (x)dx were required to have
                                      a
            finite domain of integration [a;b]
            finite integrand f (x) < ±∞
    Improper integrals
        1   Infinite limits of integration
        2   Integrals with vertical asymptotes i.e. with infinite discontinuity
            Ryan Blair (U Penn)                    Math 104: Improper Integrals               Tuesday March 12, 2013      3 / 15