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U-Substitution Homework Stu Schwartz Answers

© www.MasterMathMentor.com- 185- IllegaltopostonInternet31. Definite Integrals with u-Substitution – ClassworkWhen you integrate more complicated expressions, you use u-substitution, as we did with indefinite integration. The issue is that we are evaluating the integrated expression between two x-values, so we have to work in x. The resolution is to perform a technique called changing the limits. Changing the limits allows us to switch both the integrand and limits of integration to u without having to then switch back to xwhen the integration is performed. It is more elegant and saves a little writing. Example 1) Find a) 2x x2+1( )3dx02∫without changing limits. b) 2x x2+1( )3dx02∫by changing the limits. Example 2) Find a) x1−x2dx01∫without changing limits. b) x1−x2dx01∫by changing the limits. Example 3) Find a) sin2x dx0π4∫without changing limits. b) x dx04∫by changing the limits.

AB Calculus Manual (Revised 1/2016)

This page provides the AB Calculus Manual for the classroom - all chapters of this manual are provided as free downloads! This section is a complete high school course for preparing students to take the AB Calculus exam.

 

In addition to the Essentials section of the manual that provide complete coverage of all topics for the AB exam, there is a Non-Essentials section as well that givers topics that are relevant to AB calculus but not on the actual AP exam. There is also a Review section that goes over the most common algebraic concepts that give students trouble.

 

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Essentials

Pages 1-26

01. Introduction

02. Tangent Lines

03. Slope secant/tangent

04. Limits graphical

05. Limits Algebraic

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Pages 27-46

06. Derivative definition

07. Derivatives w/ technology

08. Differentiation techniques

09. Chain Rule

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10. Derivatives of trig functions
11. Implicit differentiation
12. Derivatives transcendentals
13. Derivatives of inverses
14. Linear approximations

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15. Continuity/differentiability
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17. Straight-line motion
18. 3 important theorems
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20. Curve sketching
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22. Optimization
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25. Indefinite integration
26. u-substitution
27. Riemann sums

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28. Definite integrals
29. Accumulation function
30. Fundamental Theorem

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31. Definite integrals u-sub
32. Integrating transcendentals
33. Motion revisited

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34. Average value, 2nd FTC
35. Inverse Trig
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Non-Essentials
Pages 241-265
1a. Introduction
12a. Logarithmic differentiation
14a. Differentials
24a. Newton's method
26a. L'Hospital advanced
29a. Exact area w/limits
37a. Volume shells

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Review
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Complex fractions
Inverses
Exponentials/logs
Graphical solutions
Sigma notation

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