invariance of formula for surface integration with respect to area under change of variables
A similar story holds for the other two factors. Combining them, we conclude that
Since the factor in parentheses in front of the square root is the Jacobi determinant, we can apply the rule change of variables in multidimensional integrals to conclude that
which shows that our formula gives the same answer for , no matter how we choose to parameterize .
|Title||invariance of formula for surface integration with respect to area under change of variables|
|Date of creation||2013-03-22 15:07:32|
|Last modified on||2013-03-22 15:07:32|
|Last modified by||rspuzio (6075)|