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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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