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Surface Integrals

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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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