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hw-07-5-integ-review

hw-07-5-integ-review - Question A The following integral is...

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Chapter 7.5 homework #2 int sin^3(x) / cos(x) dx #10 int_0^4 (x-1)/(x^2-4x-5) dx remember that the integral of 1/u is ln|u| #18 int e^(2t) / (1+e^(4t)) dt #20 int e^2 dx #27 int 1/(1+e^x) dx #30 int_-2^2 |x^2-4x| dx #36 int sin 4x cos 3x dx #43 int exp(x)*sqrt(1+exp(x)) dx #45 int x^5 * exp(-x^3) dx #69 int exp(2x)/(1+exp(x)) dx #81 The functions y=exp(x^2) and y=x^2 exp(x^2) don't have elementary antiderivatives, but y=(2x^2+1)exp(x^2) does. Find it. (You end up making a guess, checking it, seeing that it doesn't work, modifying it, and checking again. If you want a more mechanistic, guaranteed way to do it you'll have to wait until Chapter 11.9)
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Unformatted text preview: Question A: The following integral is important in a particular geometry problem (you will learn later which geometry problem): integral of sqrt(1+(bx/a)^2 * 1/(a^2-x^2) ) dx For each of the following methods, write down what happens as you try it, but don't spend very long on it. i) Try a simple u-substitution. ii) Try integration by parts. iii) Try trig substitution. iv) Any other ideas? v) optional: what if b=a? Can you simplify it and solve it? Review questions (pg 518) Concept Check: #1, #3...
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