Posted by **mathstudent** on Sunday, January 13, 2008 at 4:36pm.

Suppose that the region between the x-axis and the curve y=e^-x for x>=0 has been revolved around the x-axis. Find the surface area of the solid.

I got 3*pi

The book shows an answer of pi * [sqrt(2) + ln(1 + sqrt(2))]

Where do I go wrong? For the sides of the surface, I integrated 2*pi*e^-x over [0,inf] and got 2*pi. Then for the base of the surface, I pi*(e^0)^2 = 2*pi.

- Calculus -
**bobpursley**, Sunday, January 13, 2008 at 4:49pm
No, I dont see how you integrated that against x.

find a differential piece of the curve ds, so 2PI y ds is the surface area. Now change ds to dx, dy, where ds^2=dx^2+dy^2

Notice that dy=-y dx so

ds^2= dx^2 +Y^2 dx^2 = (1+y^2) dx^2

or ds=sqrt (1+y^2) dx

Now integrate with respect to x.

area= INT 2PI e^-x (1+e^-2x) dx from x=1 to inf

see if that helps.

Check my thinking, I haven't integrated it to check.

- Calculus -
**mathstudent**, Monday, January 14, 2008 at 1:03am
Thank you bobpursley.

My surface area integral was bad.

I was incorrectly assuming

S = Int 2*pi*f(x) dx

I read through proof. It is

S = Int 2*pi*f(x)*sqrt(1+(dy/dx)^2) dx

Thanks!

- Calculus -
**babu**, Tuesday, November 27, 2012 at 11:18pm
Gas is escaping from a spherical balloon at the rate of 2ft3/min. How fast is the

surface area shrinking when the radius is 2ft?

## Answer this Question

## Related Questions

- calculus - Find the volume of the solid that is obtained when the region under ...
- CALCULUS - The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(...
- CALCULUS HELP PLZ - The region R is bounded by the x-axis, y-axis, x = 3 and y...
- Calculus - solid is formed by rotating the region bounded by the curve y=e−...
- Calculus - solid is formed by rotating the region bounded by the curve y=e&#...
- Calculus - A solid is formed by rotating the region bounded by the curve y=e&#...
- calculus - let R be the region of the first quadrant bounded by the x-axis and ...
- AP Calculus - Let R be the region bounded by the x-axis and the graph of y=6x-x^...
- calculus - Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real ...
- Calculus - Let R be the region bounded by the x-axis, x = 5 and the curve y = x...