My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree3Thanks
  • 1 Post By v8archie
  • 1 Post By mr. jenkins
  • 1 Post By v8archie
Reply
 
LinkBack Thread Tools Display Modes
April 23rd, 2014, 06:12 AM   #1
Senior Member
 
Joined: Dec 2013

Posts: 137
Thanks: 4

Volume Problem (showing lots of work)

Here is the problem... Gyazo - 67aaed27d46cd857a41289d1def5d9d7.png

Here is what I did. To find the area of the cross-sectional area A(y), I solved the 2 given equations y = a root x and y = a x ^b for y and got

x = (y/7)^2 and
x = (y^(1/5))/7^(1/5)

now, using the washer method deal I go A(y)= (piR^2 - pir^2)dy

and came up with R = (1 - y^2 / 49) and r = (1 - y^(1/5)/7^(1/5)

now putting that all together and Integrating from 0 to 7 I quickly see that when it's time to plug and chug the 0 is going to cancel all equations thus I will have this - 0 = that so I essentially just need to lay these eq's out as pi INTEGRAL (R^3 - r^2) - (0) dy =

now is the point right before integrating where we combine equations and I am getting... (-2y^(2)/49) + (y^4)/2401 + 2y^(1/5)/(7^1/5) - y^(2/5)/7^(2/5) from 0 to 7 (again, we are just going to be plugging in the b =7 value when integrating because plugging in zero will just give 0 , thus it is unnecessary.

Now, this is the point when I started to get excited because I started to see that plugging the b value of 7 into y and CHUGGING! as you guys say ... I quickly saw that everything was canceling so nice ...almost like I had stacked a million dominos and they were all coming down in 30 secs (haha u math folks like that analagy..lol)

Anyways, very unfortuneately, I ended up with Pi (0) thus giving me 0 and I am sure that volume of this problem is not zeor.


So help you guys!
mr. jenkins is offline  
 
April 23rd, 2014, 08:55 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,341
Thanks: 2463

Math Focus: Mainly analysis and algebra
I think that you forgot to integrate!
Thanks from mr. jenkins
v8archie is offline  
April 23rd, 2014, 06:55 PM   #3
Senior Member
 
Joined: Dec 2013

Posts: 137
Thanks: 4

V8 I think you are def right.

So, I did Integrate now and got 17pi/5

Does that look right V8?
mr. jenkins is offline  
April 23rd, 2014, 07:11 PM   #4
Senior Member
 
Joined: Dec 2013

Posts: 137
Thanks: 4

V8 it is right so don't trouble yourself with it.

thanks very much for pointing out the fact that I didn't integrate. I went back and did that and got the right answer so thanks for the help
Thanks from v8archie
mr. jenkins is offline  
April 23rd, 2014, 08:36 PM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,341
Thanks: 2463

Math Focus: Mainly analysis and algebra
No problem. I'm glad to be of service.
Thanks from mr. jenkins
v8archie is offline  
April 24th, 2014, 10:48 AM   #6
Senior Member
 
Joined: Dec 2013

Posts: 137
Thanks: 4

V8 if you are still around... here is an almost identical problem but this time a different region with slightly different functions. I'm confused again on how to set it up (i.e., whether to use y or x or if I'm simply overthinking the problem)

Gyazo - bed125b39432da10902bbffa8e8c86b4.png
mr. jenkins is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
lots, problem, showing, volume, work



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
work Problem slimcan Elementary Math 5 June 17th, 2010 04:01 AM
Lots of maths scholarships vbbgold New Users 1 January 16th, 2010 06:25 PM
Lots of imaginary number problems Malgrif Algebra 5 September 17th, 2009 03:26 PM
Lots of Pre-Calculus review problems (HELP!) Jph93 Calculus 7 August 19th, 2009 06:29 PM
B-Splines Cox-DeBoor: Lots of confusion Intuition Real Analysis 0 April 14th, 2008 09:29 PM





Copyright © 2018 My Math Forum. All rights reserved.