Hence aream aream w ds m w ts tt ds dt u

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Unformatted text preview: (a + b cos t)b cos s cos tˆ + (a + b cos t)b sin s cos tj + (a + b cos t)b sin tk. ı ˆ 1 Therefore, � � �Ts × Tt � = (a + b cos t)b(cos2 s cos2 t + sin2 s cos2 t + sin2 t)1/2 = (a + b cos t)b. As a ≥ b, note that (a + b cos t)b > 0. Hence area(M ) = area(M ∩ W ) �� = dS M ∩W �� � � = �Ts × Tt � ds dt U � 2π � 2π = (a + b cos t)b ds dt 0 0 � 2π = 2πb (a + b cos t) dt 0 = 4π 2 ab. Notice that this is the surface area of a cylinder of radius b and height 2πa, as expected. Example 30.2. We can parametrise the sphere, M = { (x, y, z ) | x2 + y...
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This note was uploaded on 01/27/2014 for the course MATH 324 taught by Professor Kopp during the Winter '08 term at University of Washington.

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