calculus document

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MATHEMATICAL ANALYSIS IIINTEGRAL CALCULUSSEVER ANGEL POPESCUTo my family...........................................................................................To those who really try to put their lives in the Light ofTruth................................................ ...............................................Dedicated to the memory of my late Professor andMentor,Dr. Doc. Nicolae Popescu.ContentsPreface7Chapter 1. Indefinite integrals (Primitives, Antiderivatives)1. Definitions, some properties and basic formulas2. Some results on polynomials3. Primitives of rational functions4. Primitives of irrational and trigonometric functions5. Problems and exercises1110212747Chapter 2. Definite integrals1. The mass of a linear bar2. Darboux sums and their applications3. Lebesgue criterion and its applications4. Mean theorem. Newton-Leibniz formula5. The measure of a figure in Rn6. Areas of plane figures bounded by graphics of functions7. The volume of a rotational solid8. The length of a curve in R39. Approximate computation of definite integrals.10. Problems and exercises49495259636875858790101Chapter 3. Improper (generalized) integrals1. More on limits of functions of one variable2. Improper integrals of the first type3. Improper integrals of the second type4. Problems and exercises105105112122135Chapter 4. Integrals with parameters1. Proper integrals with parameters2. Improper integrals with paramet

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