{"id":10269,"date":"2017-06-19t15:10:20","date_gmt":"2017-06-19t22:10:20","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=10269"},"modified":"2017-06-18t16:13:38","modified_gmt":"2017-06-18t23:13:38","slug":"ap-calculus-bc-review-integration-substitution","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-bc-review-integration-substitution\/","title":{"rendered":"ap calculus bc review: integration by substitution"},"content":{"rendered":"

substitution<\/strong> is just one of the many techniques available for finding indefinite integrals<\/em> (that is, antiderivatives<\/em>). let’s review the method of integration by substitution and get some practice for the ap calculus bc exam.<\/p>\n

the substitution rule<\/h2>\n

integration by substitution, also known as u<\/em>-substitution<\/strong>, after the most common variable for substituting, allows you to reduce a complicated integral to one that is easier to work with.<\/p>\n

the formula works as follows. suppose that f<\/em> is an antiderivative for f<\/em>. then we have:<\/p>\n

\"integration<\/p>\n

in fact, you can think of the substitution rule as reversing the chain rule<\/em>.<\/p>\n

basically, this rule states that if you have a complicated integral like the one on the left, then it instantly reduces to a simpler one that can be worked out with no trouble.<\/p>\n

\n
\"surprised
okay, i’m listening.<\/figcaption><\/figure>\n<\/div>\n

however, the hard part is arranging a given integral in the right way. that’s where the step-by-step method outlined below comes in.<\/p>\n

furthermore, substituting isn’t a magic bullet that can tackle every integral. just think of it as one powerful tool in your toolbox. for more tools and information about integration, check out the following resource. ap calculus review: indefinite integrals<\/a>.<\/p>\n

the method of integration by substitution<\/h2>\n

next let’s review the main steps in u<\/em>-substitution.<\/p>\n

step 1. choose your substitution<\/h3>\n

if you want to use substitution, then the first thing to do is to identify what you want to substitute.<\/p>\n

in other words, you have to make a choice for what u<\/em> = g<\/em>(x<\/em>) will be in your integral.<\/p>\n

but what should you choose? that comes with experience.<\/p>\n

there are a few good rules of thumb to follow when choosing u<\/em>, but these are by no means fool-proof. so if the first choice doesn’t work, try something else.<\/p>\n