Homework Help Overview
The discussion revolves around evaluating a vector surface integral over a cylindrical surface defined by the equation x² + y² = 9, with z ranging from -3 to 3. The vector field in question is F(x,y,z) = . Participants are exploring the correct approach to compute the integral ∫∫S F · dS, particularly focusing on the parameterization and the orientation of the normal vector.
Discussion Character
- Exploratory, Assumption checking
Approaches and Questions Raised
- The original poster attempts to parameterize the surface using cylindrical coordinates and calculates the normal vector. They express concern over a discrepancy between their computed integral result and the expected answer.
- Some participants question whether the outward normal vector has been correctly identified and whether the problem requires consideration of the closed surface of the cylinder, including the top and bottom surfaces.
- Others suggest reconsidering the use of the divergence theorem as a potential approach to the problem.
- There is a discussion about the implications of using inward versus outward normals and how that affects the integral's sign.
Discussion Status
The discussion is active, with participants providing guidance on checking the orientation of the normal vector and clarifying the definition of the surface in the problem statement. Multiple interpretations of the problem setup are being explored, particularly regarding whether the entire cylindrical surface or just its lateral area is to be considered.
Contextual Notes
Participants note that the problem as stated may not clearly indicate whether the integral should include the top and bottom surfaces of the cylinder, leading to potential confusion about the setup. There is also mention of imposed homework rules regarding the use of calculators for evaluating integrals.