7.8 Integration Techniques
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 typebecause asymptotic value is caught in the
interval. To apply the limit, the asymptotic value needs to be determined first. The value 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. Then l’Hospital’s rule can be applied.
Determine if the integral is convergent or divergent. If convergent, evaluate the integral.