Surface Area Problem: Rotating y=x^4/16+1/2x^2 About Y-Axis

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SUMMARY

The discussion centers on calculating the surface area obtained by rotating the curve defined by the equation y = x^4/16 + 1/2x^2 for the interval 1 < x < 2 about the y-axis. The final answer presented is 41π/10, which is confirmed as correct by the participants. The problem utilizes calculus concepts, specifically the method of revolution for surface area calculations.

PREREQUISITES
  • Understanding of calculus, specifically surface area of revolution.
  • Familiarity with integral calculus and the disk method.
  • Knowledge of the function y = x^4/16 + 1/2x^2.
  • Ability to evaluate definite integrals.
NEXT STEPS
  • Study the disk method for calculating surface areas of revolution.
  • Learn about the application of definite integrals in surface area problems.
  • Explore examples of rotating different functions about the y-axis.
  • Investigate advanced topics in calculus, such as parametric equations and their surface areas.
USEFUL FOR

Students studying calculus, educators teaching surface area concepts, and anyone interested in mathematical modeling of curves and their properties.

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Homework Statement
Find the surface area obtained by rotating the curve [tex]y = \frac{x^4}{16} + \frac{1}{2x^2}[/tex] 1 < x < 2 about the y-axis.



The attempt at a solution
http://img341.imageshack.us/img341/3245/mathy.jpg

My final answer is [tex]\frac{41\pi}{10}[/tex]. Is this correct?
 
Last edited by a moderator:
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Seems right to me.
 

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