Fall 2006 - Takeda's Class - Final Exam

Fall 2006 - Takeda's Class - Final Exam - Math 20B, Final...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: Math 20B, Final Exam Solutions December 7, 2006 Name: Section: This exam consists of 11 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use two 4-by-6 index cards, both sides. 4. You have two hours for this exam. Score 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1 1. (a) Evaluate Z 2 1 x ln( x 2 ) dx Let u = x 2 . Then du = 2 xdx and x 1 2 u 1 4 Then Z 2 1 x ln( x 2 ) dx = Z 4 1 1 2 ln u du = 1 2 ( u ln u- u ) 4 1 = 1 2 [(4 ln 4- 4)- (- 1)] = 2 ln 2- 3 2 . (b) Find the indefinite integral Z xe x dx By integration by parts, Z xe x dx = xe x- e x + C. 2 2. Compute R 2 1 1 x- 1 dx . (Note: The integrand is not defined at x = 1.) Since 1 x- 1 is not defined at x = 1, this is an improper integral. Thus Z 2 1 1 x- 1 dx = lim t 1 + Z 2 t 1 x- 1 dx = lim t 1 + 2 x- 1 2 t = lim t 1 + (2- 2 t- 1) = 2 ....
View Full Document

This note was uploaded on 04/29/2008 for the course MATH 20B taught by Professor Justin during the Fall '08 term at UCSD.

Page1 / 11

Fall 2006 - Takeda's Class - Final Exam - Math 20B, Final...

This preview shows document pages 1 - 4. Sign up to view the full document.

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