CALCULUSIICH14 - CHAPTER 1 FURTHER TECHNI QUES I N...

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CHAPTER 1 FURTHER TECHNIQUES IN CONSTRUCTING ANTIDERIVATIVES
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CONTENTS 1.1. Review of Definite and Indefinite Integrals 1.2. Trigonometric Integrals 1.3. Partial Fractions 1.4. Integration Using Tables and Computer Algebra Systems 1.5. Improper Integrals.
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1.4. Integration Using Tables And Computer Algebra Systems 1.4.1. Tables of Integrals 1.4.2. Computer Algebra Systems 1.4.3. Can we Integrate all Continuous Functions
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1.4.1 Table of Integrals In Calculus I, we had seen a very brief Table of Indefinite integrals. On the Reference Pages at the back of the Text book, there is a longer table with 120 entries. There are also other standard tables with thousands of entries. When confronting an integral that is difficult to evaluate by hand, our first approach may be to look up at some table to find the entry which is closest to our integral. The Substitution Rule or
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Example. Find Solution. Entry 17 of the Table gives + + 2 0 2 2 4 12 dx x x To use it we perform long division of polynomials C a u a u a du + = + - 1 2 2 tan 1 4 8 1 4 12 2 2 2 + + = + + x x x (1) Applying formula (1) with a =2 π + = + = + = + + = + + - - 2 1 tan 4 2 2 tan 8 4 8 1 4 12 1 2 0 1 2 1 2 0 2 2 0 2 2 x x dx x dx x x
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Example. Evaluate
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CALCULUSIICH14 - CHAPTER 1 FURTHER TECHNI QUES I N...

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