Example

Section	You should be able to…	Examples	Review Exercises
7.1	1 Integrate by parts (p. 472)	1–6	8, 9, 16, 19, 21, 25, 47, 48
	2 Derive a formula using integration by parts (p. 476)	7, 8	37, 38
7.2	1 Find integrals of the form \(\int \sin ^{n}x\,dx\) or \(\int \cos ^{n}\!x\,dx,\) \(n \ge 2\) an integer (p. 480)	1–3	5, 31
	2 Find integrals of the form \(\int \sin ^{m}x\,\cos^{n}x\,dx\) (p. 483)	4	10, 28
	3 Find integrals of the form \(\int \tan ^{m}x\,\sec^{n}x\,dx\) or \(\int \cot ^{m}x\,\csc ^{n}x\,dx\) (p. 483)	5–7	3, 4
	4 Find integrals of the form \(\int \sin (ax) \sin (bx) \,dx\), \( \int \sin (ax) \,\cos (bx)\,dx,\) or \(\int \cos (ax) \,\cos (bx) \,dx\) (p. 485)	8	32, 33
7.3	1 Find integrals containing \(\sqrt{a^{2}-x^{2}}\) (p. 488)	1	6, 11
	2 Find integrals containing \(\sqrt{x^{2}+a^{2}}\) (p. 489)	2, 3	18, 24, 26
	3 Find integrals containing \(\sqrt{x^{2}-a^{2}}\) (p. 491)	4	7, 30
	4 Use trigonometric substitution to find definite integrals (p. 492)	5, 6	34, 35
7.4	1 Find an integral that contains a quadratic expression (p. 496)	1–3	1, 14, 20
7.5	1 Integrate a rational function whose denominator contains only distinct linear factors (p. 500)	1, 2	12, 27, 29
	2 Integrate a rational function whose denominator contains a repeated linear factor (p. 502)	3	17, 23
	3 Integrate a rational function whose denominator contains a distinct irreducible quadratic factor (p. 503)	4	2, 15
	4 Integrate a rational function whose denominator contains a repeated irreducible quadratic factor (p. 504)	5	22
7.6	1 Approximate an integral using the Trapezoidal Rule (p. 508)	1–5	49(a), 50
	2 Approximate an integral using Simpson’s Rule (p. 514)	6–8	49(b)
7.7	1 Use a Table of Integrals (p. 520)	1–3	36(a)
	2 Use a computer algebra system (p. 522)	4	36(b)
7.8	1 Find integrals with an infinite limit of integration (p. 524)	1, 2	39, 42, 44
	2 Interpret an improper integral geometrically (p. 525)	3, 4	51, 52
	3 Integrate functions over \([a,b]\) that are not defined at an endpoint (p. 527)	5–7	40, 41, 43
	4 Use the Comparison Test for Improper Integrals (p. 529)	8	45, 46