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Unformatted text preview: Assignment for First Two Class Meetings. Integration is far more difficult than differentiation. So to be good at integration, one should practice on it far more than on differentiation. Just inside the hard cover at the end of our textbook, there are 120 integral formulas. Of course, we do not need to memorize all of these. We can look up the less often used formulas as needed. But there is a short list of formulas used so often that the scientist simply could not afford to stop the normal flow of study to find another formula. Furthermore, a well-chosen short list must be memorized. For this list is used as a foundation to organize the overall picture of the whole integration problem. So if one does not know the basic list, then he or she would be dumbfounded as to the type of formula to look for to solve a given integral problem. At the beginning of the semester, each student is given a printed list of these basic 16 integral formulas along with some common trigonometric identities. But in case the student misplaces his or her copy, the student may print out another copy from my web page. It would be a good idea for the student to keep this list of the basic 16 integration formulas and trig identities in a special notebook for the calculus course. It is essentially impossible to be good at integration if one does not memorize the basic 16 integral formulas. This is very easy to do if we learn them in small groups as follows: B1–B3 first: then B14–B16; then B4–B9; B10–B13 last. In 1–18, find each integral simply by applying a basic integral formula without making a substitution. In order to maximize your personal growth and strength in integration, I strongly advise you not to make a substitution in these problems. To continue to substitute in these integrals, which actually fit a basic integral formula , will surely impede your progress in developing good skills for integration. In introducing some students to integration, it may be helpful to let them use the substitution method in the beginning with the hope that soon they will abandon the ”training wheels phase” of their learning process in integration; however, it is often difficult to give up bad habits!difficult to give up bad habits!...
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- Spring '08
- Calculus, dx