Question

Volumes Find the volumes of the solids in Exercises 65-70. spherical + cylindrical coordinates 65. $z = 4 - 4(x^2 + y^2)$ $z = (x^2 + y^2)^2 - 1$ 66. $z = 1 - r$ $z = -\sqrt{1 - r^2}$ 67. $r = 3 \cos \theta$ 68. $z = \sqrt{x^2 + y^2}$ $r = -3 \cos \theta$

Name: volumes find the volumes of the solids in exercises 65 70 spherical cylindrical coordinates 65 z 4 4x2 y2 z x2 y22 1 66 z 1 r z sqrt1 r2 67 r 3 cos theta 68 z sqrtx2 y2 r 3 cos theta 48754
Uploaded: 2020-11-08T02:57:53-08:00
Duration: 4 min 6 s
Channel: Chris Trentman
Description: volumes find the volumes of the solids in exercises 65 70 spherical cylindrical coordinates 65 z 4 4x2 y2 z x2 y22 1 66 z 1 r z sqrt1 r2 67 r 3 cos theta 68 z sqrtx2 y2 r 3 cos theta 48754

          Volumes
Find the volumes of the solids in Exercises 65-70. spherical + cylindrical coordinates
65.
$z = 4 - 4(x^2 + y^2)$
$z = (x^2 + y^2)^2 - 1$
66.
$z = 1 - r$
$z = -\sqrt{1 - r^2}$
67.
$r = 3 \cos \theta$
68.
$z = \sqrt{x^2 + y^2}$
$r = -3 \cos \theta$

volumes find the volumes of the solids in exercises 65 70 spherical cylindrical coordinates 65 z 4 4x2 y2 z x2 y22 1 66 z 1 r z sqrt1 r2 67 r 3 cos theta 68 z sqrtx2 y2 r 3 cos theta 48754

Added by Concepci-N J.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Chris Trentman

11/08/2020

Step 1

We need to determine the limits of integration for each problem. The problems are given in both Cartesian and cylindrical coordinates. We will choose the coordinate system that makes the integration easiest. Show more…

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Volumes Find the volumes of the solids in Exercises 65-70. spherical + cylindrical coordinates 65. $z = 4 - 4(x^2 + y^2)$ $z = (x^2 + y^2)^2 - 1$ 66. $z = 1 - r$ $z = -\sqrt{1 - r^2}$ 67. $r = 3 \cos \theta$ 68. $z = \sqrt{x^2 + y^2}$ $r = -3 \cos \theta$