hw-07-1-integ-by-parts

hw-07-1-integ-by-parts - Homework for Chapter 7.1:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

hw-07-1-integ-by-parts - Homework for Chapter 7.1:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online