MATH111-200530-PS04

MATH111-200530-PS04 - sec θ d θ 6. (1 mark) Suppose the...

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Math 111 Problem Set 4 Edward Doolittle Due: Thursday, October 20, 2005, at the beginning of tutorial Please hand the following problems in. The last two are more difficult, as usual. 1. (2 marks) 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. (2 marks) 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. (2 marks) 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. (2 marks) 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 2 π 4 cot 4 xdx 5. (1 mark) Evaluate the following integrals: (a) dx 1 sin x (b) π 4 0 tan 4 θ
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Unformatted text preview: sec θ d θ 6. (1 mark) Suppose the function 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. You do not need to hand in your solutions to these problems! 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 CALC 111 taught by Professor Edwarddoolittle during the Summer '05 term at Berkeley.

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