MATH 1591: Integration Techniques and L'Hopital's Rules - Chapter 7 Review, Study notes of Calculus

Download MATH 1591: Integration Techniques and L'Hopital's Rules - Chapter 7 Review and more Study notes Calculus in PDF only on Docsity! 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’Hôpital’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. ∫ x √ x2 − 1 dx 2. ∫ x2 sin 2x dx 3. ∫ −12 x2 √ 4−x2 dx 4. ∫ 16 0 1 4√x dx Use L’Hôpital’s Rules to evaluate the limits: 1. lim x→0 sin πx sin 2πx 2. lim x→∞ e2x x2 1