18-Integration-U-Substitution-Review - Integration by...

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Phong Do Integration by Substitution Successful integration of a problem is always a challenge for students taking Calculus. It is an understatement to say that, integration is among the most difficult concepts in Calculus that the students will encounter. This section is an attempt to provide a quick review of the integration by substitution – a method which is normally covered in Calculus I. It would be helpful to review these before moving on further. Basically, the method of substitution can be divided into 2 types: o The u-substitution o The miscellaneous substitution At the very least, students who already had Calculus I should be very familiar and comfortable in using the “u- substitution”. The best place to get to know the “ u-substitution ” starts with the Power Rule: 1 1 1 n n u u du C n n + + + ≠ − = Pay careful attention to the rule and you will note that, instead of “x” and “dx” , we use “u” and du” . And if you look more closely at ALL integration rules provided in your book and everywhere else, they all contain “u” and du”. So it is important that you know how to work with them. Below is a snapshot of several formulas from the book that you should have been exposed to back in Calculus I. To use the “ u-substitution ”, you must make sure that the “u” and the “du” are consistent. If they are NOT consistent, see if YOU can make them consistent. And to be successful, you must: o Recognize the pattern quickly o Determine the derivative quickly The best way to learn the u-substitution is to study plenty of examples and then practice! The easiest type of u-substitution problem is the ones involving polynomials. And that is where we will begin. As you go through them, pay attention to how we get the “u” and “du” to be consistent.
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