242hw6solns - Math 242 Homework 6 Solutions(to the “by...

Info iconThis preview shows pages 1–2. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 242 Homework 6 Solutions (to the “by hand” questions) Questions 1 through 5 should be done by hand. For questions 6 through 8, you can use Maple as much or as little as you like. 1. Evaluate Z sin(ln x ) dx . (May be a little tricky.) Solution. Let I = Z sin(ln x ) dx , and integrate by parts with u = sin(ln x ) and dv = 1 dx . Then du = cos(ln x ) · 1 x dx and v = x . We then have I = x sin(ln x )- Z cos(ln x ) dx. Integrate by parts again, with u = cos(ln x ) and dv = 1 dx . Then du =- sin(ln x ) · 1 x dx and v = x . This gives I = x sin(ln x )- x cos(ln x )- Z- sin(ln x ) dx I = x sin(ln x )- x cos(ln x )- Z sin(ln x ) dx 2 I = x sin(ln x )- x cos(ln x ) I = 1 2 x sin(ln x )- x cos(ln x ) + C. 2. Evaluate Z ∞ x x 2 + 2 dx or show that it is divergent. Solution. Consider Z M x x 2 + 2 dx . Substitute u = x 2 +2, so du = 2 x dx ⇒ 1 2 du = x dx . The integral becomes 1 2 Z M 2 +2 2 1 u du = 1 2 ln( M 2 + 2)- ln 2 ....
View Full Document

This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.

Page1 / 3

242hw6solns - Math 242 Homework 6 Solutions(to the “by...

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