MATH 101 Suggested Problems
Integral Calculus with Applications to Physical Sciences and Engineering
2013W Term 2
Below are some suggested problems. Mathematics is a subject that can only
be learned by doing it – the more you work problems, the better. If you
aren’t spending most of your MATH 101 study time working problems, you need to
adjust what you do when you study.
There will also be supplementary challenge-level problems posted from time-totime. These are intended to give you a flavour of the harder kinds of problems that
often appear on exams.
Week 1 Areas. The Definite Integral.
Section 5.1: 1, 3, 7, 13, 16, 19, 20, 25, 30.
Section 5.2: 3, 5, 8, 14, 17, 20, 24, 27, 33, 44, 50, 57, 63, 68.
Week 2 The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change
Theorem. The Substitution Rule.
Section 5.3: 3, 7, 10, 13, 28, 37, 43, 46, 57, 67, 77.
Section 5.4: 3, 6, 21 to 34, 39, 41, 49, 63.
Section 5.5: 2, 5, 14, 20, 21, 25 to 36, 60, 74, 79, 86, 90, 91.
Week 3 Areas between curves. Volumes.
Section 6.1: 1, 4, 9, 12, 19, 23, 26, 31, 45, 47, 55.
Section 6.2: 6, 7, 12, 19 – 30, 39, 41, 47, 61, 64, 70.
Week 4 Work. Average value of functions. Integration by parts
Section 6.4: 3, 5, 11, 13, 17, 27.
Section 6.5: 4, 7, 10, 13, 17, 19, 20, 22.
Section 7.1: 3 to 36 (!), 66, 68, 69, 70.
Week 5 Trigonometric Integrals. Inverse Trigonometric Substitutions. Partial Fractions.
Section 7.2: Do as many of the integrals in this section as you can. 56, 66, 70*.
Section 7.3: Do as many of the integrals in this section as you can. 35, 38, 39, 42.
Section 7.4: Do as many of the integrals in this section as you can. 65, 66, 72. (Number
59 is a nice problem if you are keen.)
Week 6 Improper Integrals.
Section 7.8: 1, 2, 5, 9, 11, 14, 21, 31, 39, 51, 52, 55, 62, 67, 68, 69, 78.
Week 7 Numerical Integration. Moments, Centres of Mass, and Centroids.
Section 7.7: 1, 2, 7, 9, 12, 17, 22, 29, 30, 32 (repeat this using the Trapezoid Rule
instead).
Section 8.3: 21, 22,23, 25, 27, 34, 39*, 41.
Week 8 Separable Differential Equations.
Section 9.3: 1, 3, 5, 8, 14, 15, 16, 19, 22, 33, 40, 42, 45, 54.
Weeks 9 and 10 Sequences. Series. Tests for Convergence. Power Series.
Section 11.1: 1, 2, 7, 9, 13, 17, 27, 29, 39, 49, 79, 91* (this last one is an interesting
problem).
Section 11.2: 1, 15, 17, 31, 36, 39, 45, 59, 77*, 87*.
Section 11.3: 1, 2, 5, 7, 15, 21, 23, 25,
Section 11.4: any (or all!) of the problems in 3 to 32.
Section 11.5: 1, and (or all!) of the problems between 5 and 20.
Section 11.6: 2, 3, 5, 8, 13, 25, 35.
Section 11.8: 3, 5, 7, 17, 20, 41.
Weeks 11 and 12 Power Series. Taylor and Maclaurin Series.
Section 11.8: 3, 5, 7, 17, 20, 38, 41, 42.
Section 11.9: 1, 2, 5, 11, 16, 25, 27, 31, 32, 34, 37, 39.
Section 11.10: 1, 2, 7, 8, 13, 19, 31, 33,38, 47, 50, 56, 57, 59, 62, 65, 69.