Study Guide - Test 1 (MATH-2212, Spring-2017).pdf -...

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MATH-2212: Calculus of One Variable IIStudy Guide for Test 1, Spring 2017Study 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 7.3– Trigonometric SubstitutionSection 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.Applying appropriate trigonometric substitutions in integrals involving radicals of the forma2-x2,a2+x2, orx2-a2.Partial fraction decomposition of rational functions; using partial fraction decomposition forintegration of rational functions.General strategies of integration: recognizing which method to apply.– 1–
MATH-2212: Calculus of One Variable IIStudy Guide for Test 1, Spring 2017Some 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], isgiven byA=Zba[f(x)-g(x)]dx.Theorem.The areaAof the region bounded by the curversx=f(y) andx=g(y) and the linesy=aandy=b, wherea < b,fandgare continuous on [a, b], andf(y)g(y) for ally[a, b], isgiven byA=Zba[f(y)-g(y)]dy.

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