My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree1Thanks
  • 1 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
February 14th, 2019, 10:46 PM   #1
Newbie
 
Joined: Feb 2019
From: United Arab Emirates

Posts: 1
Thanks: 0

*I need help with this problem*

Hello everyone,

So I started a mathematics research in calculus.
I was trying to find which quadratic equation that goes through point A(-5,5) and B(5,5) would give the minimum surface area of revolution.
As the general formula of a quadratic function is
f(x)=ax^2+bx+c
After putting A and B into the general formula, I found that f(x)=ax^2-25a+5 would be the general formula for the quadratic equations that pass the two points.
Using the surface area of revolution formula
I ended up at following expression (check attachment please)

So if i solved the definite integral above it would give me an expression in a and then dA/da=0 and d^2A/da^2>0 would give me the a value at which the surface area is the minimum right?
However, the integration became too complicated and that is where I'm stuck.
I did get the answer to that integral but differentiating that again is overwhelming.
So, I'm asking if there was a way to simplify the method or the calculation.

Thanks,
Josh
Attached Images
File Type: jpg Screen Shot 2019-02-15 at 11.13.01 AM.jpg (9.7 KB, 3 views)
sangbeompark13 is offline  
 
February 15th, 2019, 07:57 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,969
Thanks: 2219

Quote:
Originally Posted by sangbeompark13 View Post
. . . would give the minimum surface area of revolution.
When what part of the parabola is rotated through what angle about what line?
Thanks from topsquark
skipjack is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
calculus, differentiation or curve, integration, problem



Thread Tools
Display Modes






Copyright © 2019 My Math Forum. All rights reserved.