CALCULUS 2: TEST 1 REVIEW SHEET

Section 5.5 The Substitution Rule

-Many of the techniques we use for this test (and later tests as well) require use of this rule

- Examples New Book p. 381 # 13,32,34,36,45 (Old Book p. 392  #11,30, 32,34,41)

Section 5.6  Integration by Parts

-Choose u by LIATE!

- Examples New Book p. 387 #3,7,10,16(O.B. p. 398 #3,7,10,16,17)

Section 5.7 Additional Techniques of Integration

-Trig Integrals Exercises1,2,4,5,6 from here

-Trig Substitution Exercises 1,2,3,17 from here

Appendix G- Integration with Partial Fractions

-Look at the Appendix G worksheet, ex N.B. p. A54 7,9,11,21,23,25 (O.B. p. A57 # 7,9,11,21,23,25)

Section 5.8 Integrating using Tables

-I will provide the tables, but you will need to know how to use them

-Examples N.B p 399 #3,5,17,19.  (O.B. p. 410 #1,3, 17, 19)

Section 5.9 Approximate Integration

-Know both the Trapezoidal Rule and Simpson’s Rule

-Know how the Midpoint Rule, Trapezoidal Rule, and Simpson’s Rule compare in terms of accuracy

-Example N.B. p. 411 #3,15,28 (O.B. p. 421 #3,15,26)

Section 5.10 Improper Integrals

-Be able to determine whether an improper interval is convergent or divergent

-Examples N.B. p. 421 # 1,5,7,25,29,35 (O.B. p. 431 #1,5,7, 23,27,33)

Section 6.1 More About Areas

-Be able to graph the region enclosed by the given curves & find its area

-Examples N.B. p. 436  # 7,9,13 (O.B. p. 446 # 7,9,13)

Section 6.2 Volumes

-Be able to find volumes using washers or disks

-Examples N.B. p. 446 # 5,7,9,16 (O.B.  p. 457 # 5,7,11,13)

Section 6.4 Arc Length

-Examples N.B. p. 459 # 7,9,13 (O.B. p. 465 #5,7,9)