- #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?
Click For Summary
SUMMARY
The discussion focuses on calculating the surface area generated by rotating the curve defined by the equation y = 1 + 4x² from x = 0 to x = 8 around the y-axis. Participants emphasize the need to divide the area into horizontal slices to facilitate the integration process. The solution involves understanding the relationship between the slope of the curve and the surface area of each slice, ultimately leading to the application of integral calculus to find the total surface area.
PREREQUISITES- Understanding of integral calculus
- Familiarity with surface area calculations
- Knowledge of curve rotation concepts
- Ability to perform integration with respect to y
- Study the method of calculating surface area of revolution
- Learn about horizontal and vertical slices in calculus
- Explore the application of surface integrals in multidimensional calculus
- Practice problems involving the rotation of curves around axes
Students in multidimensional calculus courses, educators teaching surface area concepts, and anyone seeking to understand the application of integrals in calculating areas of surfaces generated by rotating curves.
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
- 2,434
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.
Similar threads
- · Replies 8 ·
- · Replies 22 ·
- · Replies 11 ·