Volumes


by Pseudo Statistic
Tags: volumes
Pseudo Statistic
Pseudo Statistic is offline
#1
Feb3-05, 10:09 AM
P: 390
I'm having trouble finding the integral I'm supposed to use for some Volume problems...
Can someone lead me in the direction as to how I should form my integrals to get the solutions?
The below is a scanned page from an AP Calculus textbook, I'm pretty much stumped on how to solve 56-59..
Hope someone can help.
Thanks.

http://www.brokendream.net/xh4/apcalcscan.jpg
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
da_willem
da_willem is offline
#2
Feb3-05, 10:47 AM
P: 603
I'll give you some hints on the first one (56a). They're all pretty much the same. The side of the squares are determined by the difference between the two functions y=x+1 and y=x^2-1. This difference is x-x^2+2, it is zero for x=-1 and x=2. So now you have determined the shape of your base.

With this you can easily find the area of such a square. Integrating over x gives you the total volume.
Pseudo Statistic
Pseudo Statistic is offline
#3
Feb3-05, 01:36 PM
P: 390
OK, so you merely evaluate the integral [tex]A (x) = \int_{-1}^\2 2 x - x^{2} + 2 dx[/tex]?
Does anybody have a clue about the other questions?
Thanks.

da_willem
da_willem is offline
#4
Feb4-05, 01:31 AM
P: 603

Volumes


Well, if you want to evalute the area enclosed by the two lines (y=..) yes, but...
Galileo
Galileo is offline
#5
Feb4-05, 03:27 AM
Sci Advisor
HW Helper
Galileo's Avatar
P: 2,004
Quote Quote by Pseudo Statistic
OK, so you merely evaluate the integral [tex]A (x) = \int_{-1}^\2 2 x - x^{2} + 2 dx[/tex]?
Does anybody have a clue about the other questions?
Thanks.
[itex]x - x^2+2[/itex] gives the length of one side of the square as a function of x. You need the area of the square.

b) Is somewhat easier, since the height of each rectangle is one, that means the area of a cross sectional rectangle is [itex]x-x^2+2[/itex].


Register to reply

Related Discussions
Volumes Calculus & Beyond Homework 6
Volumes Calculus & Beyond Homework 2
Control Volumes? Mechanical Engineering 5
Volumes Introductory Physics Homework 1
volume of the resulting solid Calculus 12