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

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SUMMARY

The discussion focuses on calculating the area that vanishes with rising tides using surface integrals. Participants agree on the importance of adjusting the limits of the inner integral to avoid negative results, emphasizing that while the size of the area is correct, the evaluation can be complex. The slope of the coast is noted to be small, approximating the area to ##\Delta(\pi r^2)##. Additionally, the value of learning LaTeX is highlighted for clearer communication in mathematical discussions.

PREREQUISITES
  • Understanding of surface integrals in calculus
  • Familiarity with integral limits and their implications
  • Basic knowledge of coastal geometry and its effects on area calculations
  • Proficiency in LaTeX for mathematical notation
NEXT STEPS
  • Research the properties of surface integrals in multivariable calculus
  • Explore techniques for evaluating integrals with variable limits
  • Study the impact of coastal slope on area calculations
  • Learn LaTeX for effective mathematical communication
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Mathematicians, physics students, and anyone involved in environmental science or coastal studies who seeks to understand surface integrals and their applications in real-world scenarios.

daphnelee-mh
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Homework Statement
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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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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.
 
andrewkirk said:
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
 
The slope of the coast is quite small, so it will be very close to ##\Delta(\pi r^2)##
 
daphnelee-mh said:
Ya, I changed the inner integral and tried to evaluate, seems hard to get a finite answer
View attachment 265808
People are answering to you even when you have not posted in latex (that’s the spirit of PhysicsForums’ users) but as a friend believe me learning latex will help you in learning more and more from this forum. People will be able to answer you more instantly and willingly.

Hoping you’re in good health and safe.
 
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