The figure shows a surface z = 8(x² + y2) and a rectangle R in the xy-plane. ZA z = 8(x² + y²) R 3 (a) Set up an iterated integral for the volume of the solid that lies under the surface and above R. dx dy (b) Evaluate the iterated integral to find the volume of the solid.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...
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The figure shows a surface

z = 8(x2 + y2)

and a rectangle R in the xy-plane. 

The figure shows a surface z = 8(x² + y2) and a rectangle R in the xy-plane.
ZA
z = 8(x² + y²)
R
3
(a) Set up an iterated integral for the volume of the solid that lies under the surface and above R.
dx dy
(b) Evaluate the iterated integral to find the volume of the solid.
Transcribed Image Text:The figure shows a surface z = 8(x² + y2) and a rectangle R in the xy-plane. ZA z = 8(x² + y²) R 3 (a) Set up an iterated integral for the volume of the solid that lies under the surface and above R. dx dy (b) Evaluate the iterated integral to find the volume of the solid.
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