chapter 3 techniques of integration 285 3 3 trigonometric substitution learning objectives 3 3 1 solve integration problems involving the square root of a sum or difference of two squares ...
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...Chapter techniques of integration trigonometric substitution learning objectives solve problems involving the square root a sum or difference two squares in this section we explore integrals containing expressions form x and wherethe values are positive have already encountered evaluated some type but many still remain inaccessible technique comes very handy when evaluating these uses to rewrite as before developing general strategy for consider integral xdx cannot be using any discussed so far however if make sin dx cos d after substituting into simplifying letting now assuming that at point can evaluate developed integrating powers products functions completing example let s take look theory behind idea asin acos see actually makes sense following argument domain is thus consequently sincetherangeof sinx over there unique angle satisfying equivalently substitute get where simplify factor out since cosx on from discussion by making able convert an radical solution back expression how ...