{"id":429,"date":"2023-11-27T18:48:46","date_gmt":"2023-11-27T18:48:46","guid":{"rendered":"https:\/\/staff.kellogg.edu\/coxaanna\/?page_id=429"},"modified":"2024-08-12T13:06:37","modified_gmt":"2024-08-12T13:06:37","slug":"math-141-calculus-1-chapter-6","status":"publish","type":"page","link":"https:\/\/staff.kellogg.edu\/coxaanna\/math-141-calculus-1-chapter-6\/","title":{"rendered":"Math 141 Calculus 1 Chapter 6"},"content":{"rendered":"\n<p><a href=\"http:\/\/www.screencast.com\/t\/sBbQqiA3e\">Section 6.1 Washer Method<\/a><br>&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/academic.kellogg.edu\/coxa\/141%20Video%20Worksheets\/Chapter%206\/MATH%20141%20Chapter%206.1%20Video%20Notes.pdf\">Worksheet for <\/a><a href=\"https:\/\/kellogg0-my.sharepoint.com\/:b:\/g\/personal\/coxa_kellogg_edu\/EYzHXODoUtJJuPKKzas3NPwBPA2PvNnDmlIqZwfhZsq1MQ?e=4zptUR\" target=\"_blank\" rel=\"noreferrer noopener\">Washer Method<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/4zOUq4Ff0B7M\">Section 6.2 Shell Method<\/a><br>&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/academic.kellogg.edu\/coxa\/141%20Video%20Worksheets\/Chapter%206\/MATH%20141%20Chapter%206.2%20Video%20Notes.pdf\">Worksheet for <\/a><a href=\"https:\/\/kellogg0-my.sharepoint.com\/:b:\/g\/personal\/coxa_kellogg_edu\/EYAs0xUpAFZNq-QVPgTAuHYBxXP8_nMXGyBu5oLrY1kO_w?e=HyoRzD\" target=\"_blank\" rel=\"noreferrer noopener\">Shell Method<\/a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/zbj2BVEU\">Section 6.3 Arc Length<\/a><br>&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/academic.kellogg.edu\/coxa\/141%20Video%20Worksheets\/Chapter%206\/MATH%20141%20Chapter%206.3%20Video%20Notes.pdf\">Worksheet for <\/a><a href=\"https:\/\/kellogg0-my.sharepoint.com\/:b:\/g\/personal\/coxa_kellogg_edu\/EdcuaqLbtP9Hgs1l_9cELvYBwblZdkguU_1WOWkJ168L7w?e=xj8lJs\" target=\"_blank\" rel=\"noreferrer noopener\">Arc Length<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/ooSOTcYV5iwD\">Section 6.4 Areas of Surfaces of Revolution<\/a><br>&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/academic.kellogg.edu\/coxa\/MATH%20141%20Chapter%206.4%20Video%20Notes.pdf\">Worksheet for <\/a><a href=\"https:\/\/kellogg0-my.sharepoint.com\/:b:\/g\/personal\/coxa_kellogg_edu\/EQ_BjGc0wcdLoYUJyAFbhggBCYuhhrYR5bl7iSWFpPU_aA?e=y6GbTz\" target=\"_blank\" rel=\"noreferrer noopener\">Areas of Surfaces of Revolution<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/fzxDfZamwlN\">Section 6.5 Work and Fluid Forces<\/a><br>&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/academic.kellogg.edu\/coxa\/MATH%20141%20Chapter%206.5%20Video%20Notes.pdf\">Worksheet for <\/a><a href=\"https:\/\/kellogg0-my.sharepoint.com\/:b:\/g\/personal\/coxa_kellogg_edu\/Ea6zczH6IdJNuxtu7RYvkOYBfO4RamSEWkCxYNQ9dTHwjQ?e=weUkwa\" target=\"_blank\" rel=\"noreferrer noopener\">Work and Fluid Forces<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/f2CkLkq9v2\">Section 6.6 Moments and Center of Mass<\/a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.screencast.com\/t\/rVptoNKF\">Generic center of mass formulas video<\/a><br>&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/academic.kellogg.edu\/coxa\/MATH%20141%20Chapter%206.6%20Video%20Notes.pdf\">Worksheet for <\/a><a href=\"https:\/\/kellogg0-my.sharepoint.com\/:b:\/g\/personal\/coxa_kellogg_edu\/EUhHTdTF5RBKim0PXzISrFAB9GdNHJi2xbQj4ngj0rgR0g?e=fNL242\" target=\"_blank\" rel=\"noreferrer noopener\">Moments and Center of Mass<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/staff.kellogg.edu\/coxaanna\/math-141-calculus-1\/\" target=\"_blank\" rel=\"noreferrer noopener\">Return to Anna&#8217;s MATH 141 page<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/staff.kellogg.edu\/coxaanna\/math-142-calculus-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">Return to Anna&#8217;s MATH 142 page<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/staff.kellogg.edu\/coxaanna\/mathematics-professor-anna-cox\/\" target=\"_blank\" rel=\"noreferrer noopener\">Return to Anna&#8217;s home page<\/a><\/p>\n\n\n\n<p>Return to&nbsp;<em><a href=\"http:\/\/www.kellogg.edu\/\">Kellogg Community College<\/a><\/em><\/p>\n\n\n\n<p>Questions asked by students<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/7d7qbMpfpbh\">Find Volume of the Described Solid 6.1-3<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/hf43gxJ9\">Circle Diameters Volume 6-1-9<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/KmxDIElTr\">Find Volume of the Solid Generated by Revolving About the X-Axis 6-1-17<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/VAsI4s4ssS\">Another Find Volume of the Solid Generated by Revolving About the X-Axis 6-1-17<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/EWIQpmywep\">Find Volume of the Solid Generated by Revolving About the Y-Axis 6-1-19<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/OIHjfAm5sZ\">Find Volume of the Solid Generated by Revolving the Region Bounded by &#8230; 6-1-21<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/xsAcIZmU\">Find the Volume of the Solid Generated by Revolving the Region in the First Quadrant &#8230; 6.1-33<\/a><\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/S7mUP1SnI\">Outer Radius Minus Inner Radius 6-1-35<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/PIzxwcgjVn1p\">Find Volume of the Solid Generated by Revolving Region about the Given Axis 6-1-47<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/TCcoyqq4c\">Find Volume of the Solid Generated by Revolving Region Bounded by the Parabola and Following Lines 6-1-51<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/rFZi2APjmSCZ\">Find the Volume that Remains After a Hole is Bored Through the Center of a Solid Sphere 6.1-51<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/EHVHIBlNf\">A Disk is Revolved about a Line to Generate a Doughnut-like Shape&#8211; Find the Volume 6-1-53<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/hI8LG4ok\">Find Volume of Water in the Hemispherical Bowl and How Fast is the Water Level Rising 6-1-54<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/JI0xllpmqD\">Use Shell Method to Find the Volume 6-2-25 part a, b, c<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/YdFvC7WeY\">Use Shell Method to Find the Volume 6-2-25 part d<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/NfVptQJcW9rd\">Use Shell and Washer Method; x-axis 6.2.29<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/EGvFmkxOv\">Use Shell and Washer Method; y-axis 6.2.29<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/hpc5uUtEiu\">Find Volume of Bead Formed from a Sphere 6.2-41<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/HWAFgd6QGtHl\">Find Volume of Water Noodle Formed by Drilling Through the Diameter of a Cylinder 6.2-41<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/XyuZbXNovO5\">Find the Length of the Curve 6-3-9<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/Gn1KVImm\">Use a Grapher to Find the Curve&#8217;s Length Numerically 6.3.15-T<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/g3uGrj9PLP\">Use a Grapher to find the Curve&#8217;s Length Numerically 6.3.16-T<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/ZCpwKv3oXdZ\">Find the Length of the Asteroid by Finding the Length of Half the First-Quadrant Portion 6-3-24<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/6KMnkaqSUsq\">Find ds^2 Where the Function s is the Arc Length Function 6.3.27<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p>6<a href=\"https:\/\/www.screencast.com\/t\/ZRY5EdEVWiC\" target=\"_blank\" rel=\"noreferrer noopener\">.3.31 arc length of first quadrant of unit circle with four line segment pieces<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/DD9XhW4dJS\" target=\"_blank\" rel=\"noreferrer noopener\">6-3-33 fundamental theorem of calculus and length of a curve<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/EkJdJNwc\" target=\"_blank\" rel=\"noreferrer noopener\">Set Up an Integral for the Area Generated by Revolving the Curve (with trig) About the x-axis 6.4.1-T<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/2m8bFq5FWqx\" target=\"_blank\" rel=\"noreferrer noopener\">Set Up an Integral for the Area Generated by Revolving the Curve About the y-axis 6.4.3-T<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/QLtVnagdNL\">Set Up an Integral for the Area Generated by Revolving the Curve (with trig) About the Y-axis 6.4.7-T<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/sYeVqce5LUC2\">Find the Surface Area of the Cone Frustum Generated by Revolving the Line Segment about the X-axis 6-4-12<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/8CBbKXqV\" target=\"_blank\" rel=\"noreferrer noopener\">Find the Surface area 6-4-13<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/WyDauRYJ\">Find the Area of the Surface Generated by Revolving about the Y-axis 6.4.19<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/V6HZ1LUSp0L\">Surface Area and Arc Length 6-4-30<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/nMbPer255dK\">Weather Dome 6-4-28\/T<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/esCfrOFA\">How Much Work to Pump Contents of Conical Container to Rim and 5 ft Above the Rim 6-5-20<\/a>&nbsp; (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/gKENUs2BLgg\" target=\"_blank\" rel=\"noreferrer noopener\">6-5-20 conic problem<\/a> \u00a0(15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/UfqdcjJJ0\">Find Work Required to Pitch a Softball a Certain Speed 6-5-30<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/screencast.com\/t\/fd1LZmztz\">Find Work Required to Project an Object at Rest to a Specific Speed 6-5-27<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p>&nbsp;<a href=\"http:\/\/www.screencast.com\/t\/3wuMFeiC\">How Many Cubic Feet Can the Isosceles end Plated Tank Hold Without Exceeding the Limitation 6-5-46<\/a> (15<sup>th <\/sup>Edition)&nbsp;<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/3wuMFeiC\">How Many Cubic Feet Can the Isosceles end Plated Tank Hold Without Exceeding the Limitation 6-5-46<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/1FfFXwNrQf\">The Region Bounded by X-axis and Curve 6-6-13<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/uLx1B85JSP\">Moment of a Wire 6-6-31<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"http:\/\/www.screencast.com\/t\/jgGx3sbQbgjp\">Center of Mass of a Wire 6-6-33<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/wspFfEBGR\">6-6-47 Center of Mass; Semicircle and X-axis<\/a> (15<sup>th <\/sup>Edition)<\/p>\n\n\n\n<p><a href=\"https:\/\/www.screencast.com\/t\/e1vGpsPKi7p8\">6-6-41 volume of a diagonal square NOT using Theorem of Pappus&nbsp; <\/a>&nbsp;(15<sup>th <\/sup>Edition)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Section 6.1 Washer Method&nbsp;&nbsp;&nbsp;&nbsp;Worksheet for Washer Method Section 6.2 Shell Method&nbsp;&nbsp;&nbsp;&nbsp;Worksheet for Shell Method&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Section 6.3 Arc Length&nbsp;&nbsp;&nbsp;&nbsp;Worksheet for Arc Length Section 6.4 Areas of Surfaces of Revolution&nbsp;&nbsp;&nbsp;&nbsp;Worksheet for Areas of Surfaces of Revolution Section 6.5 Work and Fluid Forces&nbsp;&nbsp;&nbsp;&nbsp;Worksheet for Work and Fluid Forces Section 6.6 Moments and Center of Mass&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Generic center of mass&hellip; <a class=\"more-link\" href=\"https:\/\/staff.kellogg.edu\/coxaanna\/math-141-calculus-1-chapter-6\/\">Continue reading <span class=\"screen-reader-text\">Math 141 Calculus 1 Chapter 6<\/span><\/a><\/p>\n","protected":false},"author":48,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-429","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages\/429"}],"collection":[{"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/users\/48"}],"replies":[{"embeddable":true,"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/comments?post=429"}],"version-history":[{"count":10,"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages\/429\/revisions"}],"predecessor-version":[{"id":706,"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages\/429\/revisions\/706"}],"wp:attachment":[{"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/media?parent=429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}