Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics
� Rules of integration :
n 1 n�1
1 . � x dx � x �C n �1
� �
2 . ( p�( x) � q�( x)) d x � p( x) � q( x) �C
3 . cp�( x) d x �cp( x) �C b
� � f ( x ) d x : Area under the graph of f( x ) and above the x -axis, between x� a a and x � b
� Trapezoidal Rule : a , b ( a
� b): End points n : Number of intervals b� a h � : Interval width n b
� can be estimated by h� f ( x0 ) � f ( xn) � 2 ( f ( x1 ) � f ( x2) � � f ( xn
� 1))
� f ( x ) d x a
� Estimation by Trapezoidal Rule :
1 2
1 . The estimation overestimates if the estimated value is greater than the
� b
actual value of f ( x ) d x a
2 . The estimation underestimates if the estimated value is less than the
actual value of
� More rules of integration :
� b f ( x ) d x a
� sin xdx � � cos x � C e x dx �e x �C
� cos xdx �sin x �C
1 cos x
�
�
1 dx � ln x � C x
� dx �tan x �C
Integration by substitution
2
� b
� f � ( x ) d x � f ( x ) � f ( b ) � f ( a ) a a
� Areas on x - y plane , between x� a and x� b: b 1 . � f ( x) dx
: Area between the graph of f( x ) and the x -axis a b
�
b
2 . � f ( x) � g( x) dx : Area between the graph of f( x ) and the graph of gx ( ) a
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