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Surface Integrals

Learn how to evaluate surface integrals over surfaces and find the mass of laminas using density functions. Understand parametric form and flux integrals through oriented surfaces. Detailed examples included.

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Surface Integrals

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  1. Surface Integrals

  2. Evaluating a Surface Integral Let S be a surface with equation z = g(x, y) and let R be its projection unto the xy-plane. If g, gx, and gy are continuous on R and f is continuous on S, then the surface integral of f over S is:

  3. 1. Evaluate the surface integral(Similar to p.1122 #1-4)

  4. 2. Evaluate the surface integral(Similar to p.1122 #1-4)

  5. 3. Evaluate the surface integral(Similar to p.1122 #5-6)

  6. 4. Find the mass of the surface lamina S of density ρ(Similar to p.1122 #11-12)

  7. Surface Integrals (parametric form)

  8. 5. Evaluate the integral(Similar to p.1122 #13-16)

  9. 6. Evaluate the integral(Similar to p.1122 #17-22)

  10. Evaluating a Flux Integral Let S be an oriented surface given by z = g(x, y) and let R be its projection onto the xy-plane

  11. 7. Find the flux of F through S where N is the upward unit normal vector to S(Similar to p.1122 #23-28)

  12. Summary: Surface Integrals [z = g(x,y)]

  13. Summary: Surface Integrals [parametric form]

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