- #1
Tranquility13
- 4
- 0
Homework Statement
Find the area of the surface obtained by rotating the curve
y= 1+4 x^2
from x=0 to x = 8 about the y-axis.
Calculating Surface Area by Rotating a Curve - How to Find the Surface Area?
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Homework Help Overview
The problem involves calculating the surface area generated by rotating the curve defined by the equation y = 1 + 4x² around the y-axis, specifically for the interval from x = 0 to x = 8. This falls within the subject area of multivariable calculus, particularly focusing on surface area and integration techniques.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the initial steps needed to approach the problem, with some expressing uncertainty about how to begin. Questions arise regarding the definition of surface integrals and the relevance of the course level. One participant suggests considering horizontal slices of the surface to facilitate the calculation.
Discussion Status
The discussion is ongoing, with participants exploring different interpretations and approaches to the problem. Some guidance has been offered regarding the use of horizontal slices and the relationship to surface area, but no consensus or resolution has been reached yet.
Contextual Notes
There is a note about ensuring that the problem is posted in the appropriate section for homework help, indicating a focus on more advanced topics rather than introductory material.
Find the area of the surface obtained by rotating the curve
y= 1+4 x^2
from x=0 to x = 8 about the y-axis.
- #2
Yannick
- 6
- 0
Hi
How did you try to solve it? Or don't you know how to start?
How did you try to solve it? Or don't you know how to start?
- #3
Tranquility13
- 4
- 0
Not sure how to start it.
Any assistance would be greatly appreciated.
Any assistance would be greatly appreciated.
- #4
malawi_glenn
Science Advisor
- 6,735
- 2,436
Is this multidimensional calculus course?
If it is, how is surface interagrals defined?
(post in relevant HW-section in the future, this is not introductory physics)
If it is, how is surface interagrals defined?
(post in relevant HW-section in the future, this is not introductory physics)
- #5
tiny-tim
Science Advisor
Homework Helper
- 25,837
- 258
Tranquility13 said:
Hi Tranquility13!
This is like the one about volumes.
again, divide it into horizontal slices at distance y above the x-axis, with height dy (so the slope is dy/dx).
what is the surface area of this slice (remember, it depends on the slope)?
get that, and then we'll do the integral.
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