# Tutor.com The Definite Integral Session

##### Nov. 29, 2012

Session Transcript - Math - Calculus, 11/11/2012 5:32PM - Tutor.comSession Date: 11/11/2012 5:32PM
Length: 34.4 minute(s)
Subject: Math - Calculus

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)
[00:00:00] How do you do this? [ File > http://lhh.tutor.com/SharedSessionFiles/47182371-1b3c-467e-9bfe-16fa767400cb_untitled.JPG ]

Cameron S (Tutor)
[00:00:06] Welcome to Tutor.com ! Let's get started.

Guest (Customer)
[00:00:09] ok
[00:00:24] for number 7 i thought the side length was 4-x^2
[00:00:39] and then i thought you would integrate it from 0 to 2
[00:00:42] but thats wrong

Cameron S (Tutor)
[00:01:03] OK.
[00:01:11] Which method are you using, first?
[00:01:21] Disks or cylindrical shells?

Guest (Customer)
[00:01:38] i have no idea i think its disks

Cameron S (Tutor)
[00:01:53] OK, that's what I would go with...just wanted to make sure.
[00:01:55]

Guest (Customer)
[00:01:56] ok

Cameron S (Tutor)
[00:02:11] Let me put that on the board quickly.

Guest (Customer)
[00:02:14] ok
[00:03:15] do you want me to insert the picture?

Cameron S (Tutor)
[00:03:44] There it is.

Guest (Customer)
[00:03:49] ok

Cameron S (Tutor)
[00:03:56] The picture in your file is very small for my old eyes

Guest (Customer)
[00:04:05] oh sorry

Cameron S (Tutor)
[00:04:57] First, it would go from 0 to 4 since we're integrating with respect to 'y'.
[00:05:11] Your method would work is we were revolving about the x-axis.

Guest (Customer)
[00:05:13] yes i have that part

Cameron S (Tutor)
[00:05:14] Make sense?

Guest (Customer)
[00:05:15]

Cameron S (Tutor)
[00:06:09] If that's a disk that I just drew, the radius would be the distance to the curve.

Guest (Customer)

Cameron S (Tutor)
[00:06:46] Let's check.
[00:07:20] Nice job.

Guest (Customer)
[00:07:46] thanks! i realized my mistake i was trying to do dx instead of dy

Cameron S (Tutor)
[00:08:04] Yep, it's easy to make that mistake!

Guest (Customer)
[00:08:15] so how would you do the next one?

Cameron S (Tutor)
[00:08:32] Would the next one be #8?

Guest (Customer)
[00:08:37] yes

Cameron S (Tutor)
[00:08:54] OK, let me paste in another graph.

Guest (Customer)
[00:08:57] ok

Cameron S (Tutor)
[00:10:47] That area about the x axis.
[00:10:53] Can you set up the integral?
[00:10:59] This one will be dx.

Guest (Customer)
[00:12:12] sorry i really dont know i thought it would be pi times 6radical x
[00:12:24] but now im confused

Cameron S (Tutor)
[00:12:52] ...and, of course, that gets squared.

Guest (Customer)
[00:14:50] ok so i guess my confusion comes from when do you know if its dx or dy?

Cameron S (Tutor)
[00:15:01] Ahhh....good question.
[00:15:09] Using the disk method or the washer method...
[00:15:22] If you revolve about the x-axis, it's always dx.
[00:15:33] If you revolve about the y-axis, it's always dy.

Guest (Customer)
[00:15:38] ok
[00:16:30] so i got 18pi

Cameron S (Tutor)
[00:16:36] Right!

Guest (Customer)
[00:16:52] yay

Cameron S (Tutor)
[00:16:59] Nice job.
[00:17:06] Anything else?

Guest (Customer)
[00:17:12] number 10 pleaswe

Cameron S (Tutor)
[00:17:23] OK, let me take a look.
[00:19:10] I'm trying to understand the wording here.
[00:19:26] The cross sections perpendicular to the x-axis...
[00:19:45] If those are semicircles...
[00:19:53] Not sure what they mean by that.
[00:20:26] They might mean the top half of a solid of revolution obtained by revolving that line about the x axis.

Guest (Customer)
[00:20:55] i thought they just meant use the equation for the semicircle in the integration
[00:21:09] like piside^2/2

Cameron S (Tutor)
[00:21:37] OK...that would be equivalent.
[00:21:39] Let's try it.
[00:22:33] The trick is finding the radius.
[00:22:39] Let me know if you need help with that part.

Guest (Customer)

Cameron S (Tutor)
[00:24:02] The radius will be y, but y has to be expressed in terms of x, since we're integrating using dx.

Guest (Customer)
[00:24:46] so its (6-x)/2

Cameron S (Tutor)
[00:24:53] Yes!

Guest (Customer)
[00:26:34] i dont think im getting the right answer

Cameron S (Tutor)
[00:26:47] OK, I'll put the integral on the board.

Guest (Customer)
[00:26:49] ok

Cameron S (Tutor)
[00:27:31] So far so good?

Guest (Customer)
[00:27:48] yes

Cameron S (Tutor)
[00:27:55] OK, next step...
[00:28:51] Is that what you got?

Guest (Customer)
[00:29:03] no
[00:29:23] i got 18pi

Cameron S (Tutor)
[00:29:43] OK.
[00:29:51] Where did we diverge on this one?

Guest (Customer)
[00:30:11] ok well i just put this part in my calculator.

Cameron S (Tutor)
[00:30:44] OK, let me try that too.

Guest (Customer)
[00:30:58] ok never mind i got 9pi
[00:31:01] sorry

Cameron S (Tutor)
[00:31:08] OK, no problem.
[00:31:23] Doesn't look like 9pi is a choice though.

Guest (Customer)
[00:33:14] ok i dont know how to fix it

Cameron S (Tutor)
[00:33:33] Me neither...I can't see any other way to interpret their question.

Guest (Customer)
[00:33:41] ok i think its a typo
[00:33:51] ill just ask my teacher

Cameron S (Tutor)
[00:33:56] Must be...our answer looks good.
[00:33:58] OK

Guest (Customer)
[00:34:08] thanks for your help! have a great day!

Cameron S (Tutor)
[00:34:18] You're welcome. You too!
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