[Blindmath] volume of rotational solids (calculus)

[Salisbury, Justin Mark]

Hi Alex,

    Are you taking Calculus II?  If so, I'm pretty sure that they aren't expecting you to integrate any functions that are undefined.  I'm pretty sure you'll be integrating continuous functions.  If you're asking how to know which bound lies inside the other one, that's generally a matter of a distance from the axis of rotation.  I hope that you can mentally conceptualize which functions lie inside other ones.  Otherwise, you'll have to use a distance formula to the axis of rotation for points on each equation.  If you just have the understanding that you're calculating the distance between two or more equations and then rotating it to turn area into volume, you should have a thorough enough understanding of what you're doing.  If you want to contact me off-list for humorous real-life examples, feel free.  Sighted mathematicians really only use sketches to help themselves understand what they're doing.  Many advanced mathematicians never even draw the functions before beginning their computations.  I think you'll be just fine as long as you know that you're accomplishing and know which functions lie inside the others.

Good luck!

Justin

Justin M. Salisbury
Undergraduate Student
The University Honors Program
East Carolina University
salisburyj08 at students.ecu.edu

"It is the mark of an educated mind to be able to entertain a thought without accepting it."    -Aristotle
________________________________________
From: blindmath-bounces at nfbnet.org [blindmath-bounces at nfbnet.org] on behalf of Alex Hall [mehgcap at gmail.com]
Sent: Tuesday, March 08, 2011 4:30 PM
To: Blind Math list for those interested in mathematics
Subject: [Blindmath] volume of rotational solids (calculus)

Hi all,
This is not a request for help in finding this sort of thing. Rather,
I am wondering if it can be done purely algebraically so I do not have
to try to imagine the graph. Example:

Find the volume of the solid formed by rotating the function y=x^2
around the x-axis from x=0 to x=4.

This one is a pretty simple example, and should be pi*x^5/5, I think.
This is using the Disk Method, but what happens with the Washer method
or the Shell method, where you might have space in the solid where the
function is not defined? Currently, I have to try to imagine the graph
to "see" the radius to use, any undefined portions, and so on. What I
am wondering is if anyone has dealt with this and has found any way to
do it all with algebra or some other non-graphical method. If so,
please share! Thanks.

--
Have a great day,
Alex (msg sent from GMail website)
mehgcap at gmail.com; http://www.facebook.com/mehgcap

_______________________________________________
Blindmath mailing list
Blindmath at nfbnet.org
http://www.nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
To unsubscribe, change your list options or get your account info for Blindmath:
http://www.nfbnet.org/mailman/options/blindmath_nfbnet.org/salisburyj08%40students.ecu.edu