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Unformatted text preview: Monday, January 16 Lecture 7 : Improper integrals. (Refers to section 6.6 in your text.) After having practiced the problems associated to the concepts of this lecture the student should be able to : Recognize the two different types of improper integrals, distinguish between an improper integral which converges and one which diverges, solve when possible, an improper integral Improper integrals of type I. 7.1 Definition If f ( x ) is continuous at all x such that x a , then we define We refer to this expression as an improper integral , (even though there is nothing "improper" about it). If the limit exists (i.e., is a real number) we say that the improper integral converges . If the limit is plus or minus infinity or more generally does not exists, we say it diverges . We similarly define By combining these two definitions we define We say this improper integral converges provided both improper integrals on the right exist. If just one or both of the two integrals on the right diverge then this integral diverges. 7.1.1 7....
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