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Techniques of Integration

CHAPTER7 Techniquesof Integration ,unlike differentiation,is moreofanart-formthana problemsinappliedmathematicsinvolve theintegrationoffunctionsgivenbycomplica tedformulae, beableto usetheTableseffectively. Theseare:substitution, , ( ).To integratea differen-tialf x dxwhichis notinthetable,wefirstseeka functionu u x sothatthegivendifferentialcanberewritten asa differentialg u duwhichdoesappearin ,if g u du G u C, weknowthat f x dx G u x C. x 2x 1dx ?Letu 2x 1, sothatdu 2dxandx u 1 x 2x 1dx u 12u1 2du2 14 u3 2 u1 2 du 14 25u5 2 23u3 2 C( ) 130u3 2 3u 5 C 130 2x 1 3 2 6x 2 C 115 2x 1 3 2 3x 1 C ( )whereat theendwehave replaceduby2x tanxdx ?

Techniques of Integration 7.1. Substitution Integration,unlike differentiation, is more of an art-form than a collection of algorithms. Many problems ... Example 7.4 As a circle rolls along a horizontal line, a point on the circle traverses a curve called the cycloid. A loop of the cycloid is the trajectory of a point as the circle goes through ...

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