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hw-07-2-trig-integ

# hw-07-2-trig-integ - Homework for Chapter 7.2 Trigonometric...

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Homework for Chapter 7.2: Trigonometric Integrals COMMON ERRORS ON THIS HOMEWORK: * not graphing when the problem statement says to graph (Questions 67, 68, A, B) As usual, you only need to turn in the ones whose answers aren't in the back of the book, except as noted. There is only one place on this homework you should use Integration By Parts: on one part of #56. Everywhere else, you should avoid integration by parts and use trig identities instead. There are many opportunities in this homework to use one of our favorite shortcuts: the integral of a pure sine or cosine wave over one or more full periods is zero. This saves a lot of trouble! But you can only apply it to _pure_ sine or cosine waves. sin^2 doesn't count, sin*cos doesn't count, etc. Of course, you can also apply another shortcut: the integral from -a to +a of a function that has "odd" symmetry is zero. 45: integral of sin(5x) sin(x) dx 56: integrating in various ways and comparing. Add part (e): explain how each answer is correct even if it differs from the others. (mandatory!) 66: household electricity For 67-69, a) graph the integrand at a variety of values for m and n. b) Describe any symmetry you see that might help you prove the various things that the problems ask you to prove.

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