MATH 1920 Lecture 27: Surface Integrals (17.4)

• School: Cornell University
• Department: Mathematics
• Course: MATH 1920
• Professor: Andrew Sale

Document Summary

!# gives the tangent vector to the curve. So the normal vector to the surface at = ((,() is. We say that p is a regular point if ((,() is non-zero. Example: (,) = (2 +1,5 + 1, +) at (5, 2, 3) find ( and ( Solving the system of equations, ( = 2 and ( = 1. = / # = < 32, 2,62 > plane is 3 4+ 12 = 13. At (5, 2, 3) , the normal vector is and the equation of the such that (5, 2, 3) = g. The surface area of surface s is given by the parameterization of (,) for (,) d. G is regular (except maybe on the boundary of d) () = ggh|/ #|h. For a surface parameterized as specified above by g, the surface integral of (,,) over s is: o(,)ph|/ #|h. Example: evaluate 2 where s is the portion of 2 +2 +2 =