{"id":47339,"date":"2024-06-03T22:11:46","date_gmt":"2024-06-03T22:11:46","guid":{"rendered":"https:\/\/www.oracletutoring.ca\/blog\/?p=47339"},"modified":"2024-06-03T22:11:46","modified_gmt":"2024-06-03T22:11:46","slug":"calculus-the-average-of-sinx-0-to-pi","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-the-average-of-sinx-0-to-pi\/","title":{"rendered":"Calculus: the average of sinx, 0 to pi"},"content":{"rendered":"\n<h2>Tutoring calculus, average values come up. The tutor mentions an example.<\/h2>\n<p>\nIn calculus, the average value of a function f(x) over a given interval (a,b) is sometimes defined as &int;<sub>a<\/sub><sup>b<\/sup>f(x)\/(b-a). That is, it&#8217;s the integral of the function over that interval divided by the interval&#8217;s length.<\/p>\n<p>For sinx, its integral is -cosx +C. The definite integral from 0 to pi would then be -(-1 &#8211; 1) = 2. Therefore, the average value of sinx from 0 to pi would be 2\/&pi; or approx. 0.6366.<\/p>\n<p>Source:<\/p>\n<p>Larson, Roland E. and Robert P. Hostetler. <em>Calculus, part one,<\/em> third edition. Toronto: D. C. Heath and Company, 1989.<\/p>\nJack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC. \n","protected":false},"excerpt":{"rendered":"<p>Tutoring calculus, average values come up. The tutor mentions an example. In calculus, the average value of a function f(x) over a given interval (a,b) is sometimes defined as &int;abf(x)\/(b-a). That is, it&#8217;s the integral of the function over that &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/calculus-the-average-of-sinx-0-to-pi\/\"> <span class=\"screen-reader-text\">Calculus: the average of sinx, 0 to pi<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[234],"tags":[3180,3181],"class_list":["post-47339","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-average-value-of-sin-0-to-pi","tag-calculus-definition-of-average-value"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=47339"}],"version-history":[{"count":4,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47339\/revisions"}],"predecessor-version":[{"id":47343,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47339\/revisions\/47343"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=47339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=47339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=47339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}