{"id":382,"date":"2023-11-21T21:47:52","date_gmt":"2023-11-21T21:47:52","guid":{"rendered":"https:\/\/staff.kellogg.edu\/coxaanna\/?page_id=382"},"modified":"2026-01-12T16:34:43","modified_gmt":"2026-01-12T16:34:43","slug":"math-241-calculus-3-chapter-15","status":"publish","type":"page","link":"https:\/\/staff.kellogg.edu\/coxaanna\/math-241-calculus-3-chapter-15\/","title":{"rendered":"Math 241 Calculus 3 Chapter 15"},"content":{"rendered":"\n

Section 15.1\u00a0Double and Iterated Integrals over Rectangles<\/a>
\u00a0 Worksheet<\/a> –\u00a0Double and Iterated Integrals over Rectangles<\/a><\/p>\n\n\n\n


Section\u00a015.2\u00a0Double Integrals over General Regions<\/a>
\u00a0\u00a0\u00a0\u00a0Examples on Double Integrals over General Regions<\/a>
\u00a0\u00a0\u00a0Worksheet<\/a> – Double Integrals over General Regions<\/a><\/p>\n\n\n\n


Section 15.3\u00a0Area by Double Integration<\/a>
\u00a0\u00a0\u00a0\u00a0Examples of Area by Double Integration<\/a>\u00a0
\u00a0\u00a0\u00a0\u00a0Worksheet<\/a> – Area by Double Integration\u00a0<\/a><\/p>\n\n\n\n


Section 15.4\u00a0Double Integration in Polar Form<\/a>
\u00a0Worksheet<\/a> – Double Integration in Polar Form<\/a><\/p>\n\n\n\n


Section 15.5\u00a0Triple Integrals in Rectangular Coordinates<\/a>
\u00a0\u00a0\u00a0\u00a0Worksheet<\/a> – Triple Integrals in Rectangular Coordinates<\/a><\/p>\n\n\n\n


Section 15.6\u00a0Moments and Centers of Mass<\/a>
\u00a0\u00a0\u00a0\u00a0Worksheet <\/a>– Moments and Centers of Mass<\/a><\/p>\n\n\n\n


Section 15.7\u00a0Triple Integrals in Cylindrical and Spherical Coordinates<\/a> Workshee<\/a>t – Triple Integrals in Cylindrical and Spherical Coordinates<\/a><\/p>\n\n\n\n


Section 15.8\u00a0Substitution in Multiple Integrals<\/a>
\u00a0\u00a0\u00a0Worksheet<\/a> –\u00a0Substitution in Multiple Integrals<\/a><\/p>\n\n\n\n

Homework:
Section 15.1    1, 3, 5, 7, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27
Section 15.2    1-57 every other odd (1, 5, 9, …) you should END on 57!
Section 15.3    1 – 17 odds
Section 15.4     1 – 31 odd
Section 15.5    1- 41 every other odd
Section 15.6    1-33 every other odd
Section 15.7    1-69 every other odd
Section 15.8     1, 3, 5, 7, 9 ,15<\/p>\n\n\n\n

15.1.27 sketch a volume from an equation<\/a><\/p>\n\n\n\n

15.2.57 finding volume both dxdy and dydx<\/a><\/p>\n\n\n\n

15.4.7 area using polar integrals<\/a><\/p>\n\n\n\n

15.4.15 area using polar integrals<\/a><\/p>\n\n\n\n

15.5.5 triple integration<\/a><\/p>\n\n\n\n

15.5.33 triple integration<\/a><\/p>\n\n\n\n

15.5.35 triple integration<\/a><\/p>\n\n\n\n

15.5.37 average<\/a><\/p>\n\n\n\n

15.5.41 triple integration<\/a><\/p>\n\n\n\n

15.6.27 inertia around a line of a wedge<\/a><\/p>\n\n\n\n

15.6.33 finding mass<\/a><\/p>\n\n\n\n

15.7.33 cylindrical coordinates for a volume<\/a><\/p>\n\n\n\n

15.7.53 spherical coordinates to find volume with additional method at end<\/a><\/p>\n\n\n\n

15.7.57 volume in spherical<\/a><\/p>\n\n\n\n

Return to Anna’s MATH 241 page<\/a><\/p>\n\n\n\n

Return to Anna’s home page<\/a><\/p>\n\n\n\n

Return to Kellogg Community College<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Section 15.1\u00a0Double and Iterated Integrals over Rectangles\u00a0 Worksheet –\u00a0Double and Iterated Integrals over Rectangles Section\u00a015.2\u00a0Double Integrals over General Regions\u00a0\u00a0\u00a0\u00a0Examples on Double Integrals over General Regions\u00a0\u00a0\u00a0Worksheet – Double Integrals over General Regions Section 15.3\u00a0Area by Double Integration\u00a0\u00a0\u00a0\u00a0Examples of Area by Double Integration\u00a0\u00a0\u00a0\u00a0\u00a0Worksheet – Area by Double Integration\u00a0 Section 15.4\u00a0Double Integration in Polar Form \u00a0Worksheet – Double… Continue reading Math 241 Calculus 3 Chapter 15<\/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-382","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages\/382"}],"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=382"}],"version-history":[{"count":12,"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages\/382\/revisions"}],"predecessor-version":[{"id":1056,"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/pages\/382\/revisions\/1056"}],"wp:attachment":[{"href":"https:\/\/staff.kellogg.edu\/coxaanna\/wp-json\/wp\/v2\/media?parent=382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}