160_7_68_strategies_NumericalApproxCOMPLETE.pdf - 7.6...

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7.6 Strategies for Integration: review Simplify the integrand FOIL, factor, & break up fractions Substitution for product of f g ( x ) and g 0 ( x ) Integration by Parts for products u dv when R vdu is known. Trig Identities & Reduction Formulas for products of trig functions to powers Trig Sub for a 2 - x 2 , a 2 + x 2 , x 2 - a 2 Partial Fractions for rational functions of polynomials Tangent Half-Angle for rational functions of trig functions 1
7.6 Strategies for Integration: examples Z sin( x ) 1 + cos( x ) dx Z 1 1 + cos( x ) dx Z x sec 2 ( x ) dx Z tan 5 ( x ) sec 5 ( x ) dx Z 1 x 2 + 2 x - 3 dx Z ( x + 3)( x - 1) dx 2
7.6 Strategies for Integration: integral tables & computers Tables of Integration Computer Algebra Systems 3
7.6 Using the FTC to Find Indefinite Integral Recall from section 5.5, p.326: & $ % The Fundamental Theorem of Calculus Part 2: If f is continuous on an open interval containing a , then the area function A ( x ) = Z x a f ( t ) dt is an antiderivative of f on that interval. That is, A 0 ( x ) = f ( x ), or d dx Z x a f ( t ) dt = f ( x )

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