# Area of a Surface of Revolution-Help Please

1. Mar 11, 2008

### soe236

[SOLVED] Area of a Surface of Revolution--Help Please

1. Problem: The curve y=e^(-x), x>0 is revolvd about the xaxis. Does the resultin surface have finite or infinite area? [Remember tht you can sometimes decide whether improper integral converges w/out calculating it exactly]

2. Surface area over [a,b]= 2(pi)*integral[f(x)*squareroot(1+f'(x)^2)dx]
Comparison test for improper integrals assuming f(x)>g(x)>0 for x>a: if integral[f(x)dx] on [a,infinity] converges, then integral[g(x)dx] on [a,infinity] also converges.

3. Surface area= 2(pi)*integral[e^(-x)*squareroot(1+e^(-2x))dx].. are the bounds [0,infinity]? What do I do after that to find out if it's finite or not? I'll appreciate any help. Thanks in advance

2. Mar 11, 2008

### benorin

You put down a comparison test, find something bigger than your integrand that is easy to integrate.