Math 142

Chapter 7 Homework

section

handouts

note to yourself
of due date

homework problems
A review of
Calculus I 		Math 141 Handout
of basic formulas 		before the first day of class Do the Review from Calculus I.
7.1
parts 		    For each problem, say which lesson you used:
  • Lesson 1: for ∫ 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?
3 - 19 odd, 23, 29, 31, 43, 49, 53, 63, 65.

Integration by Parts is the first (of many) techniques (of integration) we willl learn. Which technique to use on a given integral - this is easy to say in the first section since we only know one technique (a.k.a. parts) thus far. But, as we learn more, which technique should you use? The answer is in true understanding and pattern recognition (usefull skills). So, once you finish the problems assigned for this section, do the following.

  • On a piece of paper, write: Lesson 1: for ∫ xn f(x) dx . Then list out the specific integrals from the homework assignment that used Lesson 1.
  • Do the same for Lessons 2 through 5.
  • Compare the integrals on your list. Look for patterns/lessons.
  • Did this help? If not - do more problems!
7.1     A Sample Recitation Quiz over Section 7.1, along with the solution.
Would you be able to work this quiz at the end of the recitation over Section 7.1, in 10 minutes, without your books/notes?
7.2
trig integrals 		handout   1, 3, 5, 7, 9, 13, 15, 17, 21, 23, 25, 29, 37, 39, 43, 45, 55, 57, 65, 68, 70 (hint: use problem 68).
7.3
trig substitution 		handout  
  • 3, 5, 7, 13, 17, 21, 35, 39.
  • Give the problems a hard try before peeking at the sol'ns.
7.4
Partial Fractions 		handout  
  • 7, 9, 11, 17, 25, 29, 39, 57, 59.
  • The solution to a quiz over completing the square that Prof. Girardi once gave when she was so upset that her students had so much troubles with this skill from high-school algebra.
  • Give the problems a hard try before peeking at the sol'ns.
7.5
Strategy for Integration 		   
  • Read the section. A formal lecture will not be given in class. Section 7.5 is a review of Sections 7.1 - 7.4.
  • Time to test your pattern recognition skills, which is a valuable skill no matter where your academic pursuit leads you. For each of Sections 7.1 through 7.4, look over the list of integral problems and see what they have in common as to learn when the technique from that section should be applied.
  • 3, 7, 17, 23 (hint: u = 1 + x1/2), 25, 31 (hint: conjugate - multiply the numerator and denominator by (1+x)1/2), 37, 41, 45, 51, 61, 66 (hint: PFD. Do you have (strictly) bigger bottoms?. No, so first you must do LD. The PFD of the integrand is 1 + 2/(u-1) - 1/u - 1/u2. Answer is 5/6 + ln (8/3)).
7.5
Follow up 		    Need more integration practice?
Integrate each of the 81 integrals from this section!
7.6 & 7.7     skip
4.4
Indeterminate Forms and L'Hopital's Rule 		    This section was covered in Math 141 and thus will not be covered in Math 142. It is needed for Section 7.8 so, if you so need, review Section 4.4.
Perhaps some helpful handouts: Some suggestions problems from Section 4.4 of our textbook to help you review: 5, 9, 11, 15, 25, 29, 31, 43, 47, 49, 59.
pre-7.8
Improper Integrals 		quiz 2:50pm sharp on Tue 9/15. To help prepare yourself for the lecture on Improper Integrals, read the section on Improper Integrals from the textbook. You should be able to do the posted quiz (just to your left, under the handout column) before hearing the lecture over Improper Integrals. The quiz will count as a recitation quiz and is due at the beginning of class on Tue. Sept 15.
Sol'n will be posted after the quiz is due.
7.8
Improper Integrals 		lecture   1, 5, 7, 12 (ans: diverge), 13, 23, 27, 31, 35 (hint: x2 - 6x + 5 = (x-1) (x-5) ), 71, 72, 73, 74.
Remark: problems 71 - 73 are over the Laplace Transform, which is important in engineering.
Ch 7 Review
pg 518 -- 520 		    3, 5, 9, 11, 15, 19, 21, 23, 25, 41, 45

Handout of 100 Integrals


  1. The 100 integrals (along with 19 applications of integration). You should work 10 integrals a day, 7 days a week, until you finish all these integrals. (Omit numbers: 17, 51, 72, 74, 96, 97, 101-105, 112, 113.)
  2. The answers to the odd number problems.
  3. Prof. Girardi's handwritten solutions to the circled problems: # 1, 3, 7, 23, 26, 35, 36, 47, 50, 71.
  4. 28 pages of hints/answers/solutions for all (#1-119) the problems.

Findable from URL: http://people.math.sc.edu/girardi/w142.html