Exam IV Review Topics I II Optimization A Optimization Procedure page 238 Anti differentiation and Indefinite Integral A Definition B Notation Terminology C Constant of Integration D Basic Rules Table page 275 E Basic Formulas Table page 275 F Area 4 6 4 7 16 21 5 1 6 21 22 25 28 5 1 7 12 13 16 19 III Summation A Basic Rules for Summation Table page 286 B Basic Summation Formulas Table page 287 IV Riemann Sums and Definite Integral A Procedure for constructing a Riemann sum page 291 5 3 2 3 B Definition of Integral as Limiting Process of Riemann Sums page 293 C Theorem Advanced Calculus Existence of Integral page 294 D Area as an Integral Chart page 295 E Properties of Definite Integral 5 3 18 19 25 26 1 Linearity Dominance Subdivision F Total Area vs Net Area V Fundamental Theorems of Calculus A First Fundamental Theorem of Calculus page 303 B Evaluating Definite Integrals 5 4 6 15 18 20 22 26 32 35 1 Notation C Second Fundamental Theorem of Calculus page 306 5 4 39 42 1 Chain Rule Extension VI Integration by Substitution A Evaluation of Definite Integrals VII First Order Differential Equations A Definition B Notation Terminology 1 Solution General Solution Particular Solution 2 Initial Value Problem IVP C First Order Separable Equations 1 Technique for Solving 5 5 9 12 17 23 24 31 33 5 5 35 38 40 5 6 21 23 25 5 6 9 12 14 D Modeling Problems 1 Growth Decay 2 Orthogonal Trajectories VIII Mean Value Theorem for Integrals A Average Value of a Function IX Numerical Integration A Efficient Rules 1 Mid Point Rule 2 Trapezoid Rule 3 Simpson s Rule B Error Estimates 1 Mid Point Rule 2 Trapezoid Rule 3 Simpson s Rule X Natural Logarithm Definition via an Integral 5 6 51 62 5 6 39 5 7 3 9 5 7 34 5 8 3 7 5 8 19 20
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