Setting up an integral for surface area

  • Thread starter Abyssnight
  • Start date
  • #1

Homework Statement


Set up an integral that represents the area of the surface generated when the region is bounded by x + y2 = 1 and the y-axis, then rotated about the y-axis. All in one-variable.


Homework Equations


SA = 2pi [tex]\int xds[/tex]
possible x2 + y2 = r2

The Attempt at a Solution


I tried to set up an integral as a circle and somehow ended up getting 2pi[tex]\int(r/2)(2pi r) dr[/tex]

When I picture it, it would be a sphere with a radius of 1. Still don't truly understand on how to make a integral to show it
 

Answers and Replies

  • #2
I looked at it again
would one possible answer be: 4pi[tex]\int(-y^2 + 1)\sqrt{1 + 4y^2}dy[/tex]
with limits of integration (0,1)
 

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