MTH 251 Study Guide - Midterm Guide: Farad

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Miami University
MTH 251
Calculus II
Winter 2018
Term Test 2
Professor: Konstantinos Beros
Exam Guide
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Table of content:
-Section 7.8: Improper Integrals (Continue)
-Section 8.1: Arc Length
-Section 8.2: Surface Area of Solids of Revolution
-Exam Review Problems
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Section 7.8: Improper Integrals (Continue)
Definition of improper Integrals of Type 1(The interval is infinite):
i. ()
 exists for every t, then we can define ()=
lim
()
, provided that this limit exists.
ii. If the integral ()
exists for every tb, then we define ()=

lim
()
provided this limit exists.
The improper integrals, ()
and ()
 are called convergent if their respective
limits exist, and divergent if their limits do not exist.
iii. If ()
=()
 both exist then we define ()
 =
()=()

Example
+ 4 

=lim

+ 4 
To solve

use u substitution where u=, du=2zdz, and
=, so
+ 4 
=1
21
+ 4 
So, plugging this back in,
lim

+ 4 
=lim
1
21
+ 4 
lim
1
2(1
2tan2)0
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