MATH111-200630-PS04 - f is continuous and positive and has a continuous positive first derivative f on the domain a b Show that f b f a f 1 y dy b

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MATH 111 Problem Set 4 Edward Doolittle Quiz: Thursday, October 26, 2006 The following problems may appear on the quiz on Thursday, October 26. The last two are more difficult, as usual. 1. Evaluate the following indefinite integrals by integration by parts: (a) x sin7 xdx (b) re π r dr (c) cos 1 xdx (d) e 3 θ sin 2 θ d θ 2. Evaluate the following indefinite trigonometric integrals: (a) sin 2 x cos 3 xdx (b) sin 5 x cos 4 xdx (c) sin 4 θ cos 2 θ d θ (d) tan 2 t sec 4 t dt 3. Evaluate the following definite integrals by integration by parts: (a) π 0 t cos4 t dt (b) 2 1 ln x x 3 dx (c) 4 1 x 2 4 e x dx (d) 8 0 t 2 t dt 4. Evaluate the following integrals: (a) π π 2 cos xdx (b) 9 4 e x dx (c) tan 3 θ sec 3 θ d θ (d) π 4 0 tan 4 xdx 5. Evaluate the following integrals: (a) dx 1 sin x (b) π 4 0 tan 4 θ sec θ d θ 6. Suppose the function
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Unformatted text preview: f is continuous and positive and has a continuous, positive first derivative f on the domain a b . Show that f b f a f 1 y dy b f b a f a b a f x dx which gives a formula for the integral of an inverse function. Please do the following problems from the textbook. They may appear on the midterm or final exam. 8.1 C-level: 1–16, 19–26, 33–36, 41–44, 49–52, 59–61; B-level: 27–32, 45–48, 62–63; A-level: 64, 66 8.2 C-level: 1–30, 33–34, 41–43, 47, 53–56, 63–67; B-level: 31–32, 35–40, 44–46, 48; A-level: 68 1...
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This note was uploaded on 01/12/2010 for the course MATH 111 taught by Professor Doolittle during the Fall '06 term at University of California, Berkeley.

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