{"id":15392,"date":"2016-07-23T22:53:40","date_gmt":"2016-07-23T22:53:40","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=15392"},"modified":"2016-07-23T22:53:40","modified_gmt":"2016-07-23T22:53:40","slug":"calculus-the-formula-for-integration-by-parts","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-the-formula-for-integration-by-parts\/","title":{"rendered":"Calculus: the formula for integration by parts"},"content":{"rendered":"

The tutor shows the motivation behind the integration by parts formula.<\/h1>\n

Integration by parts is a reversal of the product rule<\/strong> (see my post here<\/a>).<\/p>\n

If we start with the product rule as<\/p>\n

(uv)’=uv’ + u’v<\/p>\n

then we integrate both sides, we get<\/p>\n

\u222b(uv)’=\u222buv’ + \u222bu’v<\/p>\n

Integral is opposite of derivative, so \u222b(uv)’ = uv:<\/p>\n

uv = \u222buv’ + \u222bu’v<\/p>\n

More conveniently, it can be written<\/p>\n

\u222buv’ + \u222bu’v = uv<\/p>\n

Next, subtracting \u222bu’v from both sides, we have<\/p>\n

\u222buv’ = uv – \u222bu’v<\/p>\n

The last term is usually written \u222bvu’:<\/p>\n

\u222buv’ = uv – \u222bvu’<\/p>\n

so that we have the familiar formula for integration by parts.<\/p>\n

In a coming post I’ll show an example of how to use the integration by parts formula.<\/p>\n

Source:<\/p>\n

Larson, Roland E. and Robert P. Hostetler. Calculus, 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 the motivation behind the integration by parts formula. Integration by parts is a reversal of the product rule (see my post here). If we start with the product rule as (uv)’=uv’ + u’v then we integrate both …<\/p>\n

Calculus: the formula for integration by parts<\/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":[1743,1741,1744,1742],"class_list":["post-15392","post","type-post","status-publish","format-standard","hentry","category-calculus","category-math","tag-derivation-of-integration-by-parts-formula","tag-integration-by-parts-formula","tag-motivation-of-integration-by-parts-formula","tag-reason-for-integration-by-parts-formula"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/15392","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=15392"}],"version-history":[{"count":8,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/15392\/revisions"}],"predecessor-version":[{"id":16984,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/15392\/revisions\/16984"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=15392"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=15392"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=15392"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}