# proct1 - Spring 2008 Math 152 Overview of Material for Test...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Spring 2008 Math 152 Overview of Material for Test I courtesy: Amy Austin Area 1. a.) A = integraldisplay b a [ Top − Bottom ] dx if an x-integral is preferred. b.) A = integraldisplay d c [ Right − Left ] dy if a y-integral is pre- ferred. Volume 2. a.) Disk : • V = integraldisplay b a πr 2 dx if revolving around the x axis. r = f ( x ) • V = integraldisplay d c πr 2 dy if revolving around the y axis. r = g ( y ) b.) Washer: • V = integraldisplay b a π ( R 2 − r 2 ) dx if revolving around the x axis. R = Top function; r =bottom function. • V = integraldisplay d c π ( R 2 − r 2 ) dy if revolving around the y axis. R = Right function; r =Left function. c.) Shell : • V = integraldisplay b a 2 πrhdx if revolving around the y axis. r = x , h = f ( x ) • V = integraldisplay d c 2 πrhdy if revolving around the x axis. r = y , h = g ( y ) d.) Slicing : • V = integraldisplay b a Adx if cross sections are perpendicular to the x axis, and A is the area of a cross section. • V = integraldisplay d c Ady if cross sections are perpendicular to the y axis, and A is the area of a cross section. Work 3. If the force F is constant, then the work W done in moving the object a distance d is W = Fd . 4. If the force f ( x ) is not constant, then the work W done in moving the object from x = a to x = b is W = integraldisplay b a f ( x ) dx . a.) Spring problems : The force f ( x ) needed to maintain a spring stretched x units beyond it’s natural length is f ( x ) = kx . Therefore the work W required to stretch the spring from...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

proct1 - Spring 2008 Math 152 Overview of Material for Test...

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

View Full Document
Ask a homework question - tutors are online