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 		lecture notes   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 		lecture   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 		  3, 5, 7, 13, 17, 21, 35, 39
7.4
PFD 		  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.
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 		   
  • Don't give up. Go to Cramster for help on the odd numbered assigned problems.
  • Need more practice? Work all the problems from this section!
    Here are some solutions/help.
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.
7.8
Improper Integrals 		lecture notes   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
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.
Also omit numbers: 101 - 105, 112, 113.
hints/sol'n

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