Finding the area of a disk divided by a parabola function.

Click For Summary

Homework Help Overview

The problem involves finding the area of two regions created by the intersection of a parabola, defined by the equation y=1/2 x^2, and a disk described by the inequality x^2+y^2 ≤ 8. The original poster expresses difficulty in approaching the problem due to a lack of prior experience with application problems.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants question the validity of the original poster's assertion that the parabola divides the disk into two equal areas. They suggest calculating the area under the curve and between the two functions as potential approaches. There is also a suggestion to identify the points of intersection between the curves.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the problem statement. Some participants express skepticism about the equality of the areas and suggest that there may be a transcription error in the problem as stated. No consensus has been reached regarding the correct interpretation of the problem.

Contextual Notes

There is mention of the original poster's transition between colleges and the resulting gaps in their understanding of the material, which may affect their ability to engage with the problem effectively.

Interception
Messages
15
Reaction score
0

Homework Statement


The parabola y=1/2 x^2 divides the disk x^2+y^2 <or= to 8 into two equal parts. Find the area of both parts.


Homework Equations





The Attempt at a Solution


I have no idea of how to go about solving this. We haven't done any application problems until now and when I transferred colleges they were several chapters ahead so I'm struggling as it is. If someone could give me a system to go about solving these and point me in the right direction I'd be very grateful.
 
Physics news on Phys.org
Do you know how to calculate an area under a curve?
Do you know how to calculate an area between two functions?

Those two parts don't look equal to me.
 
Drawing a picture seems like a good start. In particular, at what points do the two curves intersect?
 
mfb said:
Those two parts don't look equal to me.
Agree, this question seems wrong as stated. One of the two "halves" will contain the entire bottom half of the disk and then some.
 
I suspect a transcription error. Maybe the original says "unequal".
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
4
Views
3K
Replies
20
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K