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Lecture

# 7.8 Improper Integrals Question #5 (Medium)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
7.8 Integration Techniques Improper Integrals Question #5 (Medium): Convergent Improper Integral With Infinite Discontinuity Strategy 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. Sample Question Determine if the integral is convergent or divergent. If convergent, evaluate the integral. ∫ Sol
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