This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Name: Section Number: TA Name: Section Time: Math 20B. Midterm Exam 2 March 1, 2006 Turn off and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. 1. (6 points) Evaluate Z e i 2 x cos( x ) dx . You may leave the result in exponential form. Z e i 2 x cos( x ) dx = 1 2 Z e i 2 x ( e ix + e- ix ) dx, = 1 2 Z ( e i 3 x + e ix ) dx, = 1 2 µ 1 3 i e i 3 x + 1 i e ix ¶ , =- i 6 ( e i 3 x + 3 e ix ) . 2. (6 points) Evaluate Z 1 ( x 2 + 16) 2 dx . Introduce the substitution x = 4tan( θ ), then dx = 4sec 2 ( θ ) dθ , and x 2 + 4 2 = 4sec 2 ( θ ). Therefore, Z dx ( x 2 + 4 2 ) 2 = Z 1 (4 2 sec 2 ( θ )) 2 4sec 2 ( θ ) dθ, = 1 4 3 Z dθ sec 2 ( θ...
View Full Document
This note was uploaded on 04/29/2008 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.
- Winter '08