hw-05-5-substitution

hw-05-5-substitution - Homework for Chapter 5.5 Integration...

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Homework for Chapter 5.5: Integration by Substitution You are responsible for all of these, but you need only turn in the ones that don't have answers in the back of the book. I provide a brief description of each problem for two reasons: * so I can easily refer to them without looking them up in the book, and * so those with a different edition can tell which exercises I meant. If I mis-type an exercise description, please use what's in the book (and tell me!) ------------ Part 1 starts here ---------------------------- 5 int cos^3(theta) sin(theta)dtheta, using u=cos(theta) 9 int (3x-2)^20 dx 10 int(3t+2)^2.4 dt 12 int x/(x^2+1)^2 dx 15 int sin(pi*t) dt 16 int x/(x^2+1) dx 18 int sec(2theta) tan(2theta) dtheta 20 int dx/(ax+b), with "a" not equal to zero (not allowed to use Big 4 Formulas here!) 26 int e^cos(t) * sin(t) dt; this one is related to modeling arrival rates. 31 int cos(x)/sin^2(x) dx 32 int e^x / (e^x +1) dx; this one is related to the "logistic" curve (different than logarithm) 42 int x/(1+x^4) dx; if your first attempt doesn't work, try something else. ------------ Part 2 starts here ---------------------------- 58 int_0^1 x*exp(-x^2) dx 62 int_0^pi/2 cos(x)* sin(sin(x)) dx 70 int_0^(T/2) sin(2 pi t/T - alpha) dt Note that this is different than sin(2 pi t/(T-alpha))

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This note was uploaded on 09/08/2011 for the course MATH 121 at Eastern Michigan University.

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hw-05-5-substitution - Homework for Chapter 5.5 Integration...

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