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Exercise 1
Math Animated™
Mathematical Introduction for Physics and Engineering
by Samuel Dagan (Copyright © 2007-2020)
Chapter 2: Integration; Section 2: Definite Integrals; page 3
Beyond Riemann, Exercise 1
Question
Calculate the improper integral
if it exists, or show that it does not, in the following cases:
-
-
Reminder
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(2.2.3.2)
|
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(2.2.3.4)
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Parts 1-4
Solution of question 1
- From the definition of the hyperbolic functions
- It follows that
- We obtain therefore that
- which according to (2.2.3.4) yields
Parts 5-6
Solution of question 2
- From the definition of the hyperbolic functions
- which yields
meaning that the improper integral does not exist.
Score
By parts:
Parts 1,4,5,6 are worth 2 points each.
Parts 2,3 are worth 1 point each
By questions:
Question 1 is worth 6 points.
Question 2 is worth 4 points.