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

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

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern