{"id":788,"date":"2012-08-22T12:35:08","date_gmt":"2012-08-22T17:35:08","guid":{"rendered":"http:\/\/blogs.acu.edu\/jee99a\/?page_id=788"},"modified":"2013-03-11T14:44:15","modified_gmt":"2013-03-11T19:44:15","slug":"arc-length-and-surface-area","status":"publish","type":"page","link":"https:\/\/blogs.acu.edu\/jee99a\/courses\/calculus-ii\/arc-length-and-surface-area\/","title":{"rendered":"Arc Length and Surface Area"},"content":{"rendered":"<div class='et-box et-shadow'>\n\t\t\t\t\t<div class='et-box-content'>\u00a0<strong>Description<\/strong>: \u00a0In this lecture we develop the notion of the length of a curve as it relates to an integral calculation. \u00a0 After deriving the formula in terms of rectangular coordinates, alternate formulas are obtained for polar and parametric forms as well. \u00a0We use these formulas to describe the surface area of a figure obtained via rotation.<\/div><\/div>\n<p>&nbsp;<\/p>\n<p><a href=\"http:\/\/blogs.acu.edu\/jee99a\/files\/2012\/08\/Arclength-and-Surface-Area-Handout.pdf\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-1027\" src=\"http:\/\/blogs.acu.edu\/jee99a\/files\/2012\/08\/F11_186_L19-490x367.jpg\" alt=\"\" width=\"490\" height=\"367\" srcset=\"https:\/\/blogs.acu.edu\/jee99a\/files\/2012\/08\/F11_186_L19-490x367.jpg 490w, https:\/\/blogs.acu.edu\/jee99a\/files\/2012\/08\/F11_186_L19-75x56.jpg 75w, https:\/\/blogs.acu.edu\/jee99a\/files\/2012\/08\/F11_186_L19-300x225.jpg 300w, https:\/\/blogs.acu.edu\/jee99a\/files\/2012\/08\/F11_186_L19.jpg 865w\" sizes=\"auto, (max-width: 490px) 100vw, 490px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t<div class='tabs-left et_sliderfx_slide et_sliderauto_false et_sliderauto_speed_5000 et_slidertype_left_tabs clearfix'>\n\t\t\t\t<div class='et_left_tabs_bg'><\/div>\n\t\t\t\t<ul class='et-tabs-control'>\n\t\t\t<li><a href='#'>\n\t\t\tReadings\n\t\t<\/a><\/li> \n\t\t<li><a href='#'>\n\t\t\tHomework\n\t\t<\/a><\/li> \n\t\t<li><a href='#'>\n\t\t\tQuizzes\n\t\t<\/a><\/li>\n\t\t<\/ul> <!-- .et-tabs-control --> \n\t\t<div class='et-tabs-content'>\n\t\t\t<div class='et-tabs-content-main-wrap'>\n\t\t\t\t<div class='et-tabs-content-wrapper'>\n\t\t\t\t\t<div class='et_slidecontent'>\n\t\t\tSection 6.4\n\t\t<\/div> \n\t\t<div class='et_slidecontent'>\n\t\t\t\u00a0\n\t\t<\/div> \n\t\t<div class='et_slidecontent'>\n\t\t\t\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t<\/div> <!-- .tabs-left -->\n<p>&nbsp;<\/p>\n<h3>Video Tutorials<\/h3>\n<p><iframe loading=\"lazy\" title=\"Calculating Arc Length 1\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/2dQKukMuAzs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><iframe loading=\"lazy\" title=\"Calculating Arc Length 2\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JDuREivbJTA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><iframe loading=\"lazy\" title=\"Length of a Polar Curve 1\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7ti_pCa7FD0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><iframe loading=\"lazy\" title=\"Calculating Surface Area 1\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/rfHzWKwmUBk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<div>\n<div><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<a href='http:\/\/blogs.acu.edu\/jee99a\/courses\/calculus-ii\/statistics-of-a-function\/' class='small-button smallsilver'>\u00a0Statistics of a Function \u00bb \u00a0<\/a>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; &nbsp; &nbsp; Video Tutorials &nbsp; &nbsp;<\/p>\n","protected":false},"author":130,"featured_media":0,"parent":96,"menu_order":8,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-788","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/788","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/users\/130"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/comments?post=788"}],"version-history":[{"count":6,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/788\/revisions"}],"predecessor-version":[{"id":1026,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/788\/revisions\/1026"}],"up":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/pages\/96"}],"wp:attachment":[{"href":"https:\/\/blogs.acu.edu\/jee99a\/wp-json\/wp\/v2\/media?parent=788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}