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# Surface Area Double Integral - Vector Analysis Watch

1. I'm stuck with part 2.

I keep getting the answer as .

Basically, I assumed that the Area would be:

Eventually, I ended up with

Is my r.dS wrong, or am I going wrong somewhere else?

From here all I had to do was integrate, and it was pretty straightforward to get to as an answer.
2. The surface area is just .
3. (Original post by wanderlust.xx)

I'm stuck with part 2.

I keep getting the answer as .

Basically, I assumed that the Area would be:

Eventually, I ended up with

Is my r.dS wrong, or am I going wrong somewhere else?

From here all I had to do was integrate, and it was pretty straightforward to get to as an answer.
Your calculation is right but r.dS gives the suface integral and not
the surface itself.
As it is written calculate the
then the surface
4. So, wait, what's the difference between the surface area and the surface integral? I thought they were just the same? =/
5. (Original post by wanderlust.xx)
So, wait, what's the difference between the surface area and the surface integral? I thought they were just the same? =/
A surface is an integral over the surface, but the integrand can be any function you like, and scalar-valued or vector-valued. You can think of the surface integral as calculating an area over the surface, but attaching a weight to every point of the surface, with this weight being our function. But when finding the surface area, we naturally want this weight to be 1 everywhere.

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