Analysis and Approaches for IBDP Maths Ebook 2

a � 3tan( �3 t � C) A1 3 � 3tan( �3(0) � C) (M1) for substitution 3 � tan C 3 � tan C � tan 6 (b) C � � 6 (A1) for correct value � � � �a� 3tan ��3t� � � 6 � A1 dv � � � � 3tan ��3t � � dt � 6� � � � 3sin ��3t � � 6 dv� � � dt � � � cos��3t � � � 6 � � � � 3sin ��3t � � 6 dv � � � � � dt (A1) for correct approach � � � cos��3t � � � 6 � � � � Let u � cos��3t� �. (M1) for substitution � 6 � du � � � � � � � �3sin ��3t � � �3sin ��3t � �dt � �1�du dt � 6 � � 6 � 1 � dv� � du u v � �lnu � D � � (A1) for correct working � � � v � �ln cos ��3t � � � D � 6 � A1 [7] 15 3 � � � �ln � �ln cos��3(0) � � � D 2 � 6� (M1) for substitution 3 3 �ln � �ln � D 2 2 D � 0 (A1) for correct value � � � �v� �ln cos ��3t� � � 6 � A1 [7] www.seprodstore.com 215

Analysis and Approaches for IBDP Maths Ebook 2 | Page 225