Using Surface Integrals, calculate the area that vanishes with this rising tide

  • #1

Homework Statement:

attached below

Relevant Equations:

A=sqrt[1+(dz/dx)^2+(dz/dy)^2]dA
1593820324786.png

Please help to see whether it's correct to do in this way
 
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Answers and Replies

  • #2
andrewkirk
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Yes that looks correct to me. I would put the limits of the inner integral the other way around - highest on the top - because the integral you gave will give you a negative number. But the size will be correct, and that's what really matters.
 
  • #3
Yes that looks correct to me. I would put the limits of the inner integral the other way around - highest on the top - because the integral you gave will give you a negative number. But the size will be correct, and that's what really matters.
Ya, I changed the inner integral and tried to evaluate, seems hard to get a finite answer
1593830154785.png
 
  • #4
haruspex
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The slope of the coast is quite small, so it will be very close to ##\Delta(\pi r^2)##
 
  • #5
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Ya, I changed the inner integral and tried to evaluate, seems hard to get a finite answer
View attachment 265808
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