{"id":17034,"date":"2016-07-27T01:36:45","date_gmt":"2016-07-27T01:36:45","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=17034"},"modified":"2016-07-27T01:36:45","modified_gmt":"2016-07-27T01:36:45","slug":"calculus-integration-by-parts-how-to-integrate-xsinx","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-integration-by-parts-how-to-integrate-xsinx\/","title":{"rendered":"Calculus: integration by parts: how to integrate xsinx"},"content":{"rendered":"

The tutor shows an essential example of integration by parts.<\/h1>\n

Back in my July 23 post,<\/a> I show the formula for integration by parts as<\/p>\n

∫uv’=uv-∫vu’<\/p>\n

Let’s consider the example<\/p>\n

∫xsinxdx<\/p>\n

Integration by parts is used to integrate a product of functions. One function needs to be identified as a derivative; it’s the one you integrate. The other function will be differentiated.<\/p>\n

In the case of ∫xsinxdx, it’s best to integrate sinxdx, but differentiate x. The reason: differentiating x will get rid of it.<\/p>\n

∫xsinxdx = -xcosx – ∫-cosxdx.<\/p>\n

which becomes<\/p>\n

∫xsinxdx = -xcosx + ∫cosxdx.<\/p>\n

Since ∫cosxdx = sinx, we arrive at <\/p>\n

∫xsinxdx = -xcosx + sinx + C<\/p>\n

The + C part compensates for an unknown constant that was destroyed by the original differentiation.<\/p>\n

I’ll be talking more about integral calculus:)<\/p>\n

Source:<\/p>\n

Larson, Roland and Robert Hostetler. Calculus<\/u>, third edition.
Toronto: D C Heath and Company, 1989.<\/p>\n

Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

The tutor shows an essential example of integration by parts. Back in my July 23 post, I show the formula for integration by parts as ∫uv’=uv-∫vu’ Let’s consider the example ∫xsinxdx Integration by parts is used to integrate a product …<\/p>\n

Calculus: integration by parts: how to integrate xsinx<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[234,3],"tags":[1750],"class_list":["post-17034","post","type-post","status-publish","format-standard","hentry","category-calculus","category-math","tag-integration-by-parts"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17034","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=17034"}],"version-history":[{"count":15,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17034\/revisions"}],"predecessor-version":[{"id":17049,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17034\/revisions\/17049"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=17034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=17034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=17034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}