Calculus Study Materials: Antiderivatives, Integrals, and Volumes - Prof. Herbert Hester, Lecture notes of Calculus

A list of homework problems for a calculus course, covering topics such as antiderivatives, estimating sums, the definite integral, numerical integration, the fundamental theorem of calculus, trigonometric integrals, volumes by slicing and rotation, moments and centers of mass, integration by parts, integrals of trigonometric functions, trigonometric substitutions, integration of rational functions, and improper integrals. The document also includes information about tests and the course review.

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2012/2013

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Week
Section
Suggested Textbook Homework Prolems
4.8
Antiderivatives p. 277: 29, 35, 37, 39, 41, 45, 49, 53, 55, 59, 61, 69, 78 BST Begins 1/22
4.8
Antiderivatives p. 277: 81, 89, 92, 107, 110, 111, 113, 121, 123, 127 BST
5.1
Estimating Sums p. 296: 1, 3, 5, 7, 9, 11, 15, 17, 19 BST
5.3
The Definite Integral
p. 313: 3, 5, 7, 15, 17, 19, 51*, 53*, 54*
* - Use the definition of the definite integral to evaluate.
BST Ends 1/28 @
10:30PM
5.3
The Definite Integral p. 313: 9, 31, 33, 43, 47, 73
8.6
Numerical Integration p. 468: 3, 9, 13, 23, 25, 26
5.4
The Fundamental Theorem of Calculus p. 325: 19, 21, 23, 39, 45, 47, 53, 54 Test 1 Begins 2/6
5.4
The Fundamental Theorem of Calculus p. 325: 27, 29, 31, 33, 59, 61, 72, 77
5.5
Indefinite Integrals and the Substitution Rule p. 333: 5, 15, 18, 21, 31, 35, 47
5.5
Indefinite Integrals and the Substitution Rule p. 333: 51, 55, 61, 65, 71, 77
5.6
Substitution and Area Between Curves p. 341: 15, 19, 22, 25, 27, 31, 39 Test 1 Ends 2/15 @ 2PM
8.2
Trigonometric Integrals p. 443: 7, 9, 17, 19, 21, 22, 23
5.1, 5.3
Average Function Value p. 296: 15, 17; p. 313: 59, 60 Test 2 Begins 2/20
5.6
Substitution and Area Between Curves
p. 341: 47*, 49*, 51, 53, 57*, 61*, 67, 69, 73, 77, 91, 101
* - Set up problem only. Do not evaluate.
6.1
Volumes by Slicing and Rotation About An
Axis
p. 361: 1, 3, 5, 9, 10
6.1
Volumes by Slicing and Rotation About An
Axis
p. 361: 15, 17, 23, 25, 29*, 31, 37*, 38*, 41*, 51*, 53*, 54b Test 2 Ends 3/1 @ 2PM
6.2
Volumes by Cylindrical Shells p. 469: 3, 5, 7, 17, 28*, 29, 30*, 37
6.6
Moments & Centers of Mass
p. 396: 21, 23 and find the center of mass for the following
masses m located at points p: m1 = 6, m2 = 5, m3 = 10;
p1 = (1, 5), p2 = (3, -2), p3 = (-2, -1)
Test 3 Begins 3/6
6.6
Moments & Centers of Mass
p. 396: 1, 3, 5*, 7, 10, 12* and set up only the center of
mass of the region bounded by x = 2y and x = y^2 - 4y.
(Density = 1)
Spring Break 3 / 9 - 3 / 17
Emporium is closed.
Reopens on Monday 3 / 18 at 8:00 AM
6.6
Moments & Centers of Mass
8.1
Integration by Parts p. 436: 1, 5, 11, 13, 23
8.1
Integration by Parts p. 436: 15, 47, 29, 30, 53, 63 Test 3 Ends 3/22 @ 2PM
8.2
Integrals of Trigonometric Functions p. 443: 25, 41, 45 Test 4 Begins 3/27
8.3
Trigonometric Substitutions p. 447: 1, 3, 5, 7, 9, 17
8.3
Trigonometric Substitutions p. 447: 19, 23, 25, 29, 53
8.4
Integration of Rational Functions by Partial
Fractions
p. 454: 3, 5, 7, 11, 13, 15 Test 4 Ends 4/5 @ 2PM
8.4
Integration of Rational Functions by Partial
Fractions
p. 454: 19, 21, 23, 33, 35, 37
8.5
Integral Tables p. 460: 1, 7, 11,15, 19, 23, 29, 41, 47, 51 Test 5 Begins 4/10
Strategies for Integration p. 481: 7, 15, 21, 29, 37, 39, 77, 79, 87, 89, 93, 95, 97
4.5
Indeterminate Forms and L'Hopital's Rule p. 253: 1, 11, 13, 19, 23, 25, 29, 33, 37
4.5
Indeterminate Forms and L'Hopital's Rule p. 253: 41, 45, 51, 53, 57, 59, 69, 75, 77 Test 5 Ends 4/19 @ 2PM
8.7
Improper Integrals p. 479: 1, 9, 11, 13, 19, 21, 49
8.7
Improper Integrals p. 479: 3, 5, 25, 27, 35, 66, 67, 69 Test 6 Begins 4/24
4.5, 8.7
Review of Improper and L'Hopital's Rule
6.3, 6.5
Arc Length. Work p. 376: 1, 3, 13, 23, 24, 25, 27; p. 386: 1, 2, 3, 5, 7, 9
6.5
Work p. 386: 13, 15, 17, 18, 21 Test 6 Ends 5/3 @ 2PM
Course
Strategies for Integration
Review Course Review Final Exam: Wed, May 15
7:45 - 9:45 AM
This course partially duplicates Math 2015. In case of inclement weather, the testing schedule will NOT be adjusted.
Math 1206C - Calculus (Spring 2013, computer tested sections) Text: University Calculus, Hass, Weir & Thomas
Test 1 Material
14
4/29 - 5/3
13
4/22 - 26
15
5/6 - 5/8
1
1/22 - 25
2
1/28 - 2/1
3
2/4 - 8
4
2/11 - 15
5
2/18 - 22
6
2/25 - 3/1
7
3/4 - 8
8
3/18 - 22
9
3/25 - 29
Test 3 Material
Test 4 Material
Test 5 Material
11
4/8 - 12
12
4/15 - 19
10
4/1 - 5
Test 6 Material

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Week Section 4.8 4.8 5.1 (^) AntiderivativesAntiderivativesEstimating Sums Suggested Textbook Homework Prolems p. 277: 29, 35, 37, 39, 41, 45, 49, 53, 55, 59, 61, 69, 78p. 277: 81, 89, 92, 107, 110, 111, 113, 121, 123, 127p. 296: 1, 3, 5, 7, 9, 11, 15, 17, 19 BST Begins 1/22BSTBST 5.3 5.3 8.6 5.4 The Definite IntegralThe Definite IntegralNumerical IntegrationThe Fundamental Theorem of Calculus p. 313: 3, 5, 7, 15, 17, 19, 51, 53, 54* * - Use the definition of the definite integral to evaluate.p. 313: 9, 31, 33, 43, 47, 73p. 468: 3, 9, 13, 23, 25, 26p. 325: 19, 21, 23, 39, 45, 47, 53, 54^ BST Ends 1/28 @ 10:30PMTest 1 Begins 2/ 5.4 5.5 5.5 5.6 8.2 The Fundamental Theorem of CalculusIndefinite Integrals and the Substitution RuleIndefinite Integrals and the Substitution RuleSubstitution and Area Between CurvesTrigonometric Integrals p. 325: 27, 29, 31, 33, 59, 61, 72, 77p. 333: 5, 15, 18, 21, 31, 35, 47p. 333: 51, 55, 61, 65, 71, 77p. 341: 15, 19, 22, 25, 27, 31, 39p. 443: 7, 9, 17, 19, 21, 22, 23 Test 1 Ends 2/15 @ 2PM 5.1, 5.3 5.6 6.1 6.1 Average Function ValueSubstitution and Area Between CurvesVolumes by Slicing and Rotation About An AxisVolumes by Slicing and Rotation About An p. 296: 15, 17; p. 313: 59, 60p. 341: 47, 49, 51, 53, 57, 61, 67, 69, 73, 77, 91, 101 * - Set up problem only. Do not evaluate.p. 361: 1, 3, 5, 9, 10 Test 2 Begins 2/ 6.2 6.6 AxisVolumes by Cylindrical ShellsMoments & Centers of Mass^ p. 361: 15, 17, 23, 25, 29, 31, 37, 38, 41, 51, 53, 54bp. 469: 3, 5, 7, 17, 28, 29, 30, 37 p. 396: 21, 23 and find the center of mass for the following masses m located at points p: m1 = 6, m2 = 5, m3 = 10; p1 = (1, 5), p2 = (3, -2), p3 = (-2, -1)^ Test 2 Ends 3/1 @ 2PM Test 3 Begins 3/ 6.6 6.6 8.1 (^) Moments & Centers of Mass Spring Break 3 / 9 - 3 / 17 Moments & Centers of MassIntegration by Parts^ p. 396: 1, 3, 5, 7, 10, 12 and set up only the center of mass of the region bounded by x = 2y and x = y^2 - 4y. (Density = 1) Emporium is closed. Reopens on Monday 3 / 18 at 8:00 AM p. 436: 1, 5, 11, 13, 23 8.1 8.2 8.3 8.3 Integration by PartsIntegrals of Trigonometric FunctionsTrigonometric SubstitutionsTrigonometric Substitutions p. 436: 15, 47, 29, 30, 53, 63p. 443: 25, 41, 45p. 447: 1, 3, 5, 7, 9, 17p. 447: 19, 23, 25, 29, 53 Test 3 Ends 3/22 @ 2PMTest 4 Begins 3/ 8.4 8.4 8.5 Integration of Rational Functions by Partial FractionsIntegration of Rational Functions by Partial FractionsIntegral Tables Strategies for Integration p. 454: 3, 5, 7, 11, 13, 15p. 454: 19, 21, 23, 33, 35, 37p. 460: 1, 7, 11,15, 19, 23, 29, 41, 47, 51p. 481: 7, 15, 21, 29, 37, 39, 77, 79, 87, 89, 93, 95, 97 Test 4 Ends 4/5 @ 2PMTest 5 Begins 4/ 4.5 4.5 8.7 (^) Indeterminate Forms and L'Hopital's RuleIndeterminate Forms and L'Hopital's RuleImproper Integrals p. 253: 1, 11, 13, 19, 23, 25, 29, 33, 37p. 253: 41, 45, 51, 53, 57, 59, 69, 75, 77p. 479: 1, 9, 11, 13, 19, 21, 49 Test 5 Ends 4/19 @ 2PM 4.5, 8.7 6.3, 6.5^ 8.7 6.5^ Improper IntegralsReview of Improper and L'Hopital's RuleArc Length. WorkWork p. 479: 3, 5, 25, 27, 35, 66, 67, 69p. 376: 1, 3, 13, 23, 24, 25, 27; p. 386: 1, 2, 3, 5, 7, 9p. 386: 13, 15, 17, 18, 21 Test 6 Begins 4/24Test 6 Ends 5/3 @ 2PM Course Review (^) This course partially duplicates Math 2015. Strategies for IntegrationCourse Review (^) In case of inclement weather, the testing schedule will NOT be adjusted. Final Exam: Wed, May 15 7:45 - 9:45 AM

Math 1206C - Calculus (Spring 2013, computer tested sections) Text: University Calculus, Hass, Weir & Thomas

Test 1 Material

141315 4/29 - 5/3^ 4/22 - 26 5/6 - 5/

(^56) 2/18 - 22 2/25 - 3/1^ Test 2 Material (^7) 3/4 - 8 (^89) 3/18 - 22 3/25 - 29

Test 3 Material Test 4 Material (^1112) 4/8 - 12 Test 5 Material 4/15 - 19

Test 6 Material