Calculus 3 Timed Quiz 6

Proposition (Surface Area) Assume that the function has  __________  partial derivatives and in a region of the -plane. Then the portion of the surface that lies over has ____________ area

Proposition (Surface Area Defined Parametrically) Let be a surface defined ____________________ by     on the region in the -plane, and assume that is smooth in the sense that and are continuous with on Then the surface area, is given by



The quantity is called the _________________ cross product.

Proposition (Fubini's Theorem for Triple Integrals) If is continuous over a rectangular box : then the triple integral may be evaluated by the iterated integral



The iterated integral can be performed in any order, with appropriate adjustments to the limits of integration.

Proposition (Triple Integrals Over z-Simple Regions) Suppose is a solid region bounded below by the surface and above by the surface that projects onto the region in the -plane. If is either type I (vertically simple) or type II (horizontally simple region), then the triple integral of the _________________ function over is

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Calculus 3 Timed Quiz 6
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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