L36 (T) - Calculus MTH 3100 Chapter 7 Techniques of Integration L36 7.6 Parts Integration by Integration by parts is a rule that transforms the

L36 (T) - Calculus MTH 3100 Chapter 7 Techniques of...

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Calculus MTH 3100 Chapter 7 : Techniques of Integration 7.6 Integration by Parts Integration by parts is a rule that transforms the integral of products of functions into simpler, integrals. The rule arises from the product rule of differentiation. dx du v dx dv u uv dx d ) ( Integrating the above equation : du v dv u uv dx dx du v dx dx dv u dx uv dx d ) ( Rewrite the last equation, we obtain du v uv dv u Integration by Parts formula Example : Evaluate dx xe x 2 L36 138 L36
Calculus MTH 3100 Chapter 7 : Techniques of Integration Example:Evaluate dxxln 2
Calculus MTH 3100 Chapter 7 : Techniques of Integration anddxxduxusincosxxevdxedvthensincoscosdxxexedxxexxxsin)cossin(sindxxexexedxxexxxxcossinsin2xexedxxexxx121)cos(sin21sinexxedxxexxL36140
Calculus MTH 3100 Chapter 7 : Techniques of Integration ______________________________________ ________________________________ Exercises : Evaluate the following integrals ; a) dx e x x 3 b) dx x x ln c) ) 1 ln( x e x d) dx x e 1 2 ) (ln e) dx x 1 tan f) dx x ) sin(ln g) dx x x 3 2 ) 1 2 ( h) e dx x 1 2 ) 1 ln( L36 141

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