# Volume of parametrized manifold

• beastmaster

#### beastmaster

I don't think this is a difficult problem, but I am not sure about what is being asked in the question. I got it from Munkres' Analysis on Manifolds page 193 Q 2.

## Homework Statement

Let A be open in R^k; let f : A-->R be of class C^r; let Y be the graph of f in R^(k+1), parametrized by the function @(x) = (x, f(x)). Express V(Y@) as an integral. (this is the volume of the graph of f)

## Homework Equations

the volume of a parametrized manifold, or V(Y@) = integral over A of det((D@)^tr D@), where D@ is the derivative matrix of @ and D@^tr is the transpose of D@.

## The Attempt at a Solution

I think I would just use the above equation to express V(Y@) as an integral. But then I would be done a little too quickly, so I thought that maybe I am supposed to simplify the matrix multiplication or something. Am I missing something here?

Also, can someone tell me how to post using mathematical symbols?

Can anyone confirm I am on the right track or am I way off? Or, at the very least, can someone tell me how to post using mathematical symbols. I am not very computer savvy. :)