Math 142

Chapter 7 Homework

section

handouts

note to yourself
of due date

homework problems
Math 141 Formulas Math 141 Handout
of basic formulas 		  An informative quiz that Prof. Girardi once gave after she was so upset with the students' performance on the exam problem of fill in the blanks of formulas from the Math 141 Handout of basic formulas.
A review of
Math 141 		    Math 141, Calculus I, covers the following sections:
1.1 - 1.5, 2.1 - 2.8, 3.1 - 3.6, 3.9, 4.1 - 4.5, 4.7, 4.9, 5.1 - 5.5, 6.1, 6.2.
  • Review the sections you need to review.
  • Read and work exercises from any section that you have not seen before.
  • Do the following problems as a Review of Math 141 Basic Skills needed for Chapter 7.
    • Section 5.3 (Fundamental Theorem of Calculus/FTC): 9, 13, 57, 59.
    • Section 5.5 (Substitution): 13, 17, 19, 25, 33, 43, 59, 67, 81, 88 (hint: cos(x) = sin (π/2 - x) and so ∫ 0π/2 f(cos(x)) dx = ∫ 0π/2 f(sin (π/2 - x)) dx and to integrate the latter let u = π/2 - x)
Math 141
Basic Skills
extra-practice problems
(optional) 		    Extra practice with u-du substitution, solutions included.
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.
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
lecture notes 		  3, 5, 7, 13, 17, 21, 35, 39
7.4
PFD 		handout
lecture notes 		  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.
  • 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)).
7.6 & 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 		    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 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.
Also omit numbers: 101 - 105, 112, 113.
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/w142.html