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Unformatted text preview: PRINT NAME: Solutions Calculus IV  Quiz III Tuesday, April 4, 2000 Q1]... Write the following triple integral out as a spherical coordinates triple integral. Z 3- 3 Z 9- x 2 Z 9- x 2- y 2 z ( x 2 + y 2 + z 2 ) dzdydx Soln: The region is precisely one quarter of a solid ball which is centered on the origin and has radius 3. The quarter is is above the xy-plane and to the positive y half of the xz-plane. The spherical coordinates description of this region is just 3 , , / 2 . Noting that the integrand converts into cos ( 2 ), and remembering that dv = 2 sin ddd , we obtain Z / 2 Z Z 3 5 cos sin ddd. Q2]... Sketch the region which is described in the following triple integral. Z / 4 Z / 2 Z sec 2 sin ddd Soln: We build the region up from small blocks which radiate outwards from the origin ( = 0) until the horizontal plane z = 1 ( = sec ). We see this last fact from the definition of spherical coordinates as follows:)....
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- Winter '08