Using a Surface Integral for Mathematical Analysis of the Area of an Island

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Homework Help Overview

The discussion revolves around the application of surface integrals in the mathematical analysis of the area of an island, specifically focusing on the shape of the island being modeled as an upside-down paraboloid.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the requirements of the problem, with some questioning the limits of integration and their implications for the integral's outcome. Others are exploring the relationship between the integral and the geometric shape of the island.

Discussion Status

The discussion is ongoing, with participants providing links for further exploration and engaging in a dialogue about the correct setup of the integral. There is acknowledgment of potential errors in the limits of integration, but no consensus has been reached.

Contextual Notes

Some participants express uncertainty about the problem's requirements and the implications of the integral's limits, indicating a need for further clarification and exploration of assumptions.

daphnelee-mh
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Homework Statement
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Relevant Equations
A=sqrt[1+(dz/dx)^2+(dz/dy)^2]dA
1593786915216.png

I am not clearly understand what the question requests for, is it okay to continue doing like this ? Kindly advise, thanks
 
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The shape of the island is an upside-down paraboloid. The integral looks like everything is OK except the ##r## limits should be reversed. You want to integrate from the smallest to largest values of ##r## to get a positive answer.
 
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LCKurtz said:
The shape of the island is an upside-down paraboloid. The integral looks like everything is OK except the ##r## limits should be reversed. You want to integrate from the smallest to largest values of ##r## to get a positive answer.
I believe you're right. I looked at it wrong.
 

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