Integral Calculus (Chapters 5+)

Section 5.1:

Notes on the reading: This section draws pretty heavily on sigma (summation) notation. The section occasionally references specific expressions that are counter-intuitively equivalent to long sums of terms (see p. 370 for an example). It is not necessary to have these formulas memorized in order to succeed in this chapter. On the other hand, it is useful to have a good understanding of sigma notation. I strongly recommend that you read through Appendix E (p. A37-A40).

p. 376: 3,11,15,17,18,19

Optional:

  • Consider solving #12 by writing a short program in python.
  • Challenge: #20. This one is even, so here’s the solution: The solution to part b.) should be 1/4.

Section 5.2:

p. 388: 1,7,9,15,17,19

(Hint for # 19: see example 2 and example 3, part a. Also, Theorem 3 c on page A40 in the appendix),…

21, 25, 29, 30, 37, 38, 39,41,43,44,45,47,49,51,55

(Hint for #55: To find the value M in property 8, find the critical numbers on [0,2] then use the techniques for finding maxima and minima from the last chapter).

Section 5.3:

You might have noticed that this is about something called ‘The Fundamental theorem of Calculus’. If you guessed that this is important, you were right!

p. 398: 1,3,5,7,9,11 (see ex. 3, p. 395), 17, 21, 27, 31, 33, 39, 43,

47 (This problem combines techniques from #9 and #11),55

Optional: 60 (This one is similar to #47), 64

 

Section 5.4:

p. 407: 1,5,7,11,13,14,19,29,35,47-53 all, 55,57

Section 5.5:

p. 417: 1,3,6,9,11,13,19,21,49,59,75,77

 

Section 5.6:

p.425 read the last proof in section 5.6 on page 425.

Chapter 5 Review:

p.427: #2,7,17,29,37,51,58,59

 

Chapter 6

Section 6.1:

p.438: #1,3,6,17,19,21,41, 45

Section 6.2:

p.448: #5,7,8,11,17,37,39,41,47

 

Section 6.3:

p.454: #1,2,3,9,21,23,29,41,43