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Homework for Chapter 7.1: Integration by Parts
COMMON ERRORS ON THIS HOMEWORK:
* getting numeric answers that violate basic bounds, e.g. on #20,
or are way too close to zero, e.g. on Question B.
For the problems that involve a little bit of numeric computation,
feel free to use Excel or some other similar program.
You need only turn in the ones that don't have answers in the
back of the book.
I strongly encourage you to check your integrations by taking the
derivative to make sure you get the original function back.
Some of your grade on this assignment will consist of doing
such double-checking.
Drill problems:
-------------------
Part I starts here ----------------------
2: int theta cos(theta) dtheta; u=theta, dv=cos(theta) dtheta
4: int x exp(-x) dx; this occurs in probability
5: int r exp(r/2) dr; again, common in probability theory
6: int t sin(2t) dt
10: int arcsin(x) dx
17: int exp(2t) sin(3t) dt
18: int exp(-t) cos(2t) dt; this integral is used in
queueing systems whose arrival rate varies by time of day.
-------------------
Part II starts here ----------------------
20: int_0^1 (x^2+1) exp(-x) dx
(first, establish LB and UB)
25: int_0^1 y/exp(2y) dy
34: int t^3 exp(-t^2) dt
39: int (2x+3)exp(x) dx; after integrating, graph integrand
and your result to make sure answer is reasonable
48: prove: int x^n exp(x) dx = x^n exp(x) - n int x^(n-1) exp(x) dx
Applied problems:

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