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MATH 2B Study Guide - Midterm Guide: Indeterminate Form, Squeeze Theorem, Product RulePremium


Department
Mathematics
Course Code
MATH 2B
Professor
Timmy Ma
Study Guide
Midterm

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University of California
Irvine
MATH 2B
Single-Variable Calculus
Fall 2017
Term Test 2
Prof: Timmy Ma
Exam Guide

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Outline
- Section 5.5 Substitution
- Section 6.1 Area between Curves
- Section 6.2 Volumes
- Section 6.5 - Average Value
- Section 7.1 - Integration by Parts
- Section 7.2 -Trig Integrals
- Section 7.3 - Trig Substitution
- Section 7.4 - Partial Fraction Decomposition
- Section 7.5/7.8 - Improper Integrals
- Section 11.1 Sequences
- Midterm 2 Review

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Section 5.5 Substitution
Review
What is the chain rule?
Take the derivative of () = (2)
′() = (2) 2
Undoing the chain rule
Is harder to recognize when to undo the chain rule when finding the integral
Instead, you can rewrite certain parts
(2)2 =
()
How?
Set = 2
Then take derivative of u

 = 2
Then isolate du
 = 2
And substitute
()
Finish taking integral
() +
Replace u’s
(2) +
Examples
7()2()
= 
 = 2
7
(1
88) +
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