Math 142

Chapter 8 Homework

section

note to yourself
the date assigned

problems
8.1
a review
of Ch. 6 		  You should be able to do these problems after you have completed Chapter 6.
No knowledge of Chapter 7 is needed.
To help you out, here are my class lecture notes for Section 8.1.
1, 3, 5, 9, 11, 13, 15, 19, 23, 25, 27, 29
8.1
a review
of Ch 6 		  A quiz that Prof. Girardi once gave after she was so upset with the students' performance on exam problems from Section 8.1.
8.1
optional
extra-practice problems 		  If you want extra practice with u-du substitution, then work through the even numbered problems from Section 8.1 (but omit # 26).
Hints and solutions to the even problems.
8.2
parts 		  For each problem, say which lesson you used:
  • Lesson 1: for ∫ xn f(x) dx ∫ xn f(x) dx
    try u = xn and dv = f(x) dx ... provided you can find v = ∫ f(x) dx
  • Lesson 2: creatively look for a dv that is easy to integrate ... for then v = ∫ dv .
  • Lesson 3: bring to the other side idea
  • Lesson 4: for ∫ f(x) dx
    if the integrand y = f(x) is easy to differentiate but hard to integrate, then try letting u = f(x) and so dv = dx.
  • Lesson 5: none of the above lessons. So what did you learn from this problem?
1, 7, 9, 13, 17, 21, 23, 27, 33, 35, 51, 55, 57, 58, 59
Give numbers 57, 58, 59 a good shot before looking at these hints .
8.3
trig integrals 		  1, 3, 5, 11, 13, 19, 27, 31, 37, 49, 55, 57
8.4
trig substitution 		  3, 5, 7, 9, 17, 19, 23, 25, 27, 29, 35, 37, 43
Give the problems a good honest hard try before looking at these hints .
8.5
PFD 		  9, 13, 17, 21, 25, 29, 31, 33, 35
Give the problems a good honest hard try before looking at these hints .
The solution to the quiz over completing the square ... which caused more trouble for some than it should have ... this is high-school algebra.
8.6   skip
8.8
improper integrals 		  1, 3, 7, 13 (draw yourself a graph), 15, 19, 21, 25, 33, 41, 45a, 57, 67.
You might need to review L'Hopital's rule (section 4.4). Here is a summary of it.
Give the problems a good honest hard try before looking at these hints .
8.7
numerical integration 		  problems
Calculators allowed on parts so indicated.
solutions
Chapter 8 Review
(for § 8.7) 		  Ch 8 Review problems, number 41 bc and 43 bc.
Chapter 8 Review
(§ 8.7 omitted) 		  3, 5, 9, 11.
15 - 31 odd.
47, 49, 51.
54 a (parts, u=x, dv = sin x dx) ,
54 b (u-sub., u = sin x or u = cos x),
54 d (u-sub., u = tan x or u = sec x),
54 e (u-sub., u = x^3 + 1),
54 f (partial fractions),
54 g (parts, u = arctan x, dv = dx),
54 h (trig. sub., x= 2 sin (theta)),
54 i (u-sub., u = 4-x^2).
55, 59, 61, 63, 69, 71, 73.
Give the problems a good honest hard try before looking at these hints .

Handout of 100 integral :     The Problems     and     Their Solutions

Handout of 100 integral   The circled ones: 1, 3, 7, 23, 26, 35, 36, 47, 50, 71.
Prof. Girardi's handwritten solutions to the circled ones.
Handout of 100 integral   You should work 10 problems a day, 7 days a week, until you finish all these problems. But do omit numbers: 17, 51, 72, 74, 96, 97.
hints to 1 - 35.
hints to 36 - 60.
hints to 60 - 83.
hints to 84 - 102.
hints to 102 - 114.
hints to 114 - 119.

Findable from URL: http://www.math.sc.edu/~girardi/
Last Modified (on or after): 12 October 2006