integration - Trig identities ? • Integration is the...

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Integration Integration Look for Strategy for Solution ( 29 x f ( 29 dx x f ( 29 x f ( 29 dx x f Remember the result n x c n x n + + + 1 1 n ax c n x a n + + + 1 1 x 1 c x + ln x sin c x + - cos x e c e x + x cos c x + sin x 2 sec c x + tan 2 1 1 x - c x + - 1 sin 2 1 1 x + c x + - 1 tan 2 1 1 x - - c x + - 1 cos ( 29 dx x - 3 4 5 dx x - 2 1 dx e x 5 dx x 3 sin Substitution – ie, change variable Inspection – use standard result, replace x by the linear function of x , and divide by coefficient of x in linear function dx x x x - + + 1 3 3 2 2 dx x x - 1 3 2 Log of denominator dx x x 2 sin cos dx xe x 2 Standard integrals Similar to standard integrals but contain a function of a linear function of x Product in which one factor comes from derivative of the other Quotient in which numerator is derivative of denominator d
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Focus on the factor whose derivative appears alongside Substitution dx x x ln 3 dx x x cos Integrate by parts dx dx du v uv dx dx dv u - = dx x x x - - - 4 3 5 2 Partial fractions dx x + 1 1 dx x 2 cos Substitution ?
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Unformatted text preview: Trig identities ? • Integration is the reverse of differentiation • As you integrate, think – the result, when differentiated, should give you the expression you are trying to integrate • Check the result by differentiating it • Can any algebraic manipulation be performed before integrating? eg, multiplying out brackets, splitting a single fraction into a sum of separate fractions if denominator contains one factor eg, ( 29 x x x x x x x 1 2 1 2 1 2 2 +-= +-=-JC2004 Quotient – more complicated than previous ones Product in which one factor is not the derivative of the other Forms different to those above, integration of trig functions...
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This note was uploaded on 04/25/2010 for the course MATH 201 taught by Professor Any during the Spring '10 term at Westminster UT.

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integration - Trig identities ? • Integration is the...

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