Study Guide - Test 1 (MATH-2212, Fall-2018).pdf - MATH-2212...

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MATH-2212: Calculus of One Variable IIStudy Guide for Test 1, Fall 2018Study Guide for Test 1It goes without saying that mathematics develops cumulatively, and all subsequent topics usuallydepend heavily on some (if not all) previous material. This study guide is intended to emphasizethe new material learned in this portion of the course. Knowing and understanding everything thathas been covered before — in prerequisite courses and earlier in this course — is also crucial forsuccess on this test.Test ContentsSection 6.1– Areas Between CurvesSection 6.5– Average Value of a FunctionSection 7.1– Integration by PartsSection 7.2– Trigonometric IntegralsSection 7.4– Integration of Rational Functions by Partial FractionsSection 7.5– Strategy for IntegrationKey ConceptsThe area between curves as a definite integral.The average value of a function; the Mean Value Theorem for Integrals.The method of Integration by Parts.Methods for integrating certain powers and products of trigonometric functions.Partial fraction decomposition of rational functions; using partial fraction decomposition forintegrating rational functions.General strategies of integration: recognizing which method to apply.Some Important Definitions, Formulas, and PropertiesTheorem.The areaAof the region bounded by the curversy=f(x) andy=g(x) and the linesx=aandx=b, wherea < b,fandgare continuous on [a, b], andf(x)g(x) for allx[a, b], is– 1–
MATH-2212: Calculus of One Variable IIStudy Guide for Test 1, Fall 2018

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