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

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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...
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This note was uploaded on 02/11/2009 for the course ENTC 219 taught by Professor Staff during the Spring '08 term at Texas A&M.

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

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