aq3 - PRINT NAME Solutions Calculus IV[2443–002 Quiz III...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PRINT NAME: Solutions Calculus IV [2443–002] 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 ≤ ρ ≤ 3 , ≤ θ ≤ π , ≤ φ ≤ π/ 2 . Noting that the integrand converts into ρ cos φ ( ρ 2 ), and remembering that dv = ρ 2 sin φdρdθdφ , we obtain Z π/ 2 Z π Z 3 ρ 5 cos φ sin φdρdθdφ. Q2]... Sketch the region which is described in the following triple integral. Z π/ 4 Z π/ 2 Z sec φ ρ 2 sin φdρdθdφ Soln: We build the region up from small blocks which radiate outwards from the origin ( ρ = 0) until the horizontal plane z = 1 ( ρ = sec φ ). We see this last fact from the definition of spherical coordinates as follows:)....
View Full Document

This note was uploaded on 01/12/2010 for the course MATH 241 taught by Professor Teleman,c during the Winter '08 term at Berkeley.

Ask a homework question - tutors are online