Analysis and Approaches HL Practice Paper Book | Page 37

www . seprodstore . com 25 � Rules of integration : 1 1 d 1 n n x x x C n � � � � � ( ( ) ( )) d ( ) ( ) p x q x x p x q x C � � � � � � � cos d sin x x x C � � � ( ) d ( ) cp x x cp x C � � � � sin d cos x x x C � � � � � � ( ) d ( ) ( ) ( ) b b a a ^{f x x f x f b f a � � � �} � 2 1 d tan cos x x C x � � � Integration by substitution d x x e x e C � � � 1 _{d ln x x C} x � � � � More integration rules : 2 sec d tan x x x C � � � 2 cosec d cot x x x C � � � � sec tan d sec x x x x C � � � cosec cot d cosec x x x x C � � � � d ln x x a a x C a � � � 2 1 d arcsin 1 x x C x � � � � 2 1 _{d arctan} 1 x x C x � � � � � Integration by parts : 1 . d du u v uv v � � � � 2 . � � d du b b b a a a u v uv v � � � � � Areas on x - y plane , between x a � and x b � : 1 . ( ) d b a ^{f x x} � : Area under the graph of ( ) f x and above the x -axis 2 . ( ) d b a ^{f x x �} � : Area under the x -axis and above the graph of ( ) f x 3 . ( ( ) ( )) d b a f x g x x � � : Area under the graph of ( ) f x and above the graph of ( ) gx 21 Applications of Integration