MATH 1591 - Review of Chapter 7
1 Main Topics
1. Integration techniques:
•Fitting integrands to basic rules on page 485.
•Integration by parts, Theorem 7.1 on page 488.
•Guidelines for trigonometric integrals on pages 497 and 500.
•Trigonometric substitutions on page 506.
•Partial fractions on page 516.
2. L’Hˆopital’s Rules for computation of limits on page 531.
3. Definitions of improper integrals on pages 540 and 543.
2 Representative Examples
1. Section 7.1: Examples 2, 4, 6.
2. Section 7.2: Examples 1, 2, 4.
3. Section 7.3: Examples 1, 2, 3, 4, 5, 6, 7, 8.
4. Section 7.4: Examples 1, 2, 4.
5. Section 7.5: Examples 1, 2, 3, 4.
6. Section 7.7: Examples 1, 2, 4, 5, 6, 7.
7. Section 7.8: Examples 1, 4, 6, 8, 9.
3 Review Exercises
Do the exercises on pages 550 and 551: 1, 5, 7, 10, 12, 13, 17, 18, 20, 22, 23, 25, 27, 31, 33,
71, 73, 75, 79, 81.
Evaluate the following integrals:
1. Rx√x2−1dx
2. Rx2sin 2x dx
3. R−12
x2√4−x2dx
4. R16
0
1
4
√x
dx
Use L’Hˆopital’s Rules to evaluate the limits:
1. lim
x→0
sin πx
sin 2πx
2. lim
x→∞
e2x
x2
1