MAT136H1 Lecture Notes - Improper Integral, Asymptote, Antiderivative

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #5 (medium): convergent improper integral with infinite discontinuity. When dealing with type improper integrals, the interval usually does not contain infinity but is over numeric values. It is categorized as improper integral of type because asymptotic value is caught in the interval. To apply the limit, the asymptotic value needs to be determined first. The value of that makes the denominator is the value the limit should approach. Once the limit is set, split the interval with respect to the asymptote, or if one end of the interval is the asymptote, replace that value with variable. Then disregard the limit and evaluate the integral. Add the anti-derivative to the limit, then plug in the approaching value to see if it diverges or converges. Sometimes directly plugging in the value cannot be done. Determine if the integral is convergent or divergent. Therefore the beginning of the interval is associated with the limit.