The surface area is another numerical quantity which should depend only on the surface itself, and not on how it is parameterized. If the surface is parameterized by the function over the domain in the -plane, then the surface area of is given by the integral

where denotes the cross product, and the absolute value denotes the length of a vector in Euclidean space. By Lagrange's identity for the cross product, the integral can be written

where is the determinant.

Area
ভূমিকা
স্থানাঙ্ক রূপান্তরের অধীনে পরিধির চাপের ধ্রুবক
Examples