Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics
� 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
� Areas on x - y plane , between y� c and y� d : d
1 . � g ( y ) d y : Area on the left of the graph of g( y ) and on the right of the c y -axis
2 . � d
� g ( y ) d y c of g( y ) d
: Area on the left of the y -axis and on the right of the graph
3 . � ( g( y) � f ( y)) dy : Area on the left of the graph of g( y ) and on the c right of the graph of f( y )
� Volumes of revolutions about the x -axis, between x� a and x� b: 1 .
2 . b
2
( ( )) d a
V � �� f x x : Volume of revolution when the region between the
graph of f( x ) and the x -axis is rotated 360 about the x -axis b
2 2
(( ( )) �( ( )) ) d a
�
V �� f x g x x : Volume of revolution when the region between the graphs of f( x ) and gx ( ) is rotated 360 about the x -axis
� Volumes of revolutions about the y -axis, between y� c and y� d : 1 .
2 . d
2
( ( )) d c
V � �� g y y : Volume of revolution when the region between the
graph of g( y ) and the y -axis is rotated 360 about the y -axis d
2 2
(( ( )) �( ( )) ) d c
�
V �� g y f y y : Volume of revolution when the region between the graphs of g( y ) and f( y ) is rotated 360 about the y -axis
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