hw5 - Homework Assignment 5 – Integration with Powers of...

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Unformatted text preview: Homework Assignment 5 – Integration with Powers of Trig Functions 1. ∫ cos 2 x sin 3 x dx 1 1 a. − cos3 x + cos5 x + C 3 5 1 1 3 b. cos x − cos5 x + C 3 5 1 1 c. − sin 3 x + sin 5 x + C 3 5 13 15 d. sin x − sin x + C 3 5 e. None of these 2. ∫ sin 2 x cos3 x dx 1 1 a. − cos3 x + cos5 x + C 3 5 1 1 b. cos3 x − cos5 x + C 3 5 1 1 c. − sin 3 x + sin 5 x + C 3 5 13 15 d. sin x − sin x + C 3 5 e. None of these 3. ∫ sin 3 a. b. c. d. e. x dx 1 x − cos3 x + C 3 1 − x + cos3 x + C 3 13 x − sin x + C 3 1 − x + sin 3 x + C 3 None of these 4. ∫ cos 3 a. b. c. d. e. 5. ∫ tan 3 a. b. c. d. e. 6. ∫ sec 4 a. b. c. d. e. 7. ∫ sec 4 a. b. c. d. e. x dx 1 x − cos3 x + C 3 1 − x + cos3 x + C 3 1 x − sin 3 x + C 3 1 − x + sin 3 x + C 3 None of these x dx 1 x − tan 3 x + C 3 1 − x + tan 3 x + C 3 1 tan 2 x − ln | sec x | +C 2 1 tan 2 x + ln | sec x | +C 2 None of these xdx = 13 tan x + tan x + C 3 15 1 tan x + tan 7 x + C 5 7 1 1 tan 2 x + tan 4 x + C 2 4 x + tan x + C None of these x tan xdx = 13 tan x + tan x + C 3 1 1 tan 2 x + tan 4 x + C 2 4 15 1 tan x + tan 7 x + C 5 7 x + tan x + C None of these 8. ∫ sec 4 a. b. c. d. e. 9. ∫ sin 2 a. b. c. d. e. x tan 4 xdx = 15 1 tan x + tan 7 x + C 5 7 13 tan x + tan x + C 3 1 1 tan 2 x + tan 4 x + C 2 4 x + tan x + C None of these x dx 1 1 x − sin x cos x + C 2 2 1 1 x + sin x cos x + C 2 2 1 x − sin x cos x + C 2 1 x + sin x cos x + C 2 None of these 10. ∫ sec x dx = a. tan x + C 1 b. tan 2 x + C 2 c. ln | sec x + tan x | +C d. ln | sec x − tan x | +C e. None of these ...
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