Your Practice Paper – Analysis and Approaches SL for IBDP Mathematics
� Rules of integration : 1 n �1
� n n�1
� x dx � x �C
( �( ) �( )) d ( ) ( ) p x � q x x � p x � q x �C
� cos xdx � sin x �C cp�( x) d x �cp( x)
�C sin xdx � � b
� cos x � C f � ( x ) d x � � f b ( x ) � � f ( b ) � f ( a ) a a
1 cos x
� dx �tan x �C
Integration by substitution
2
� x x e dx �e �C
�
�
�
1 dx � ln x � C x
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Applications of Integration
� Areas on x - y plane , between x� a and x� b: b
1 . � f ( x ) d x : Area under the graph of f( x ) and above the x -axis a
2 . � b
� f ( x ) d x : Area under the x -axis and above the graph of f( x ) a b
3 . � ( f ( x) � g( x)) dx : Area under the graph of f( x ) and above the graph of a gx ( )
� Applications in kinematics :
1 . at (): Acceleration with respect to the time t
2 . |
v( t)
� � a( t) dt
: Velocity
|
3 . |
s( t)
� � v( t) dt
: Displacement
|
4 . t2 d � � v( t) dt
: Total distance travelled between t 1 and t 2 t1
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