Analysis and Approaches for IBDP Maths Ebook 2 | Page 180

Your Practice Set – Analysis and Approaches for IBDP Mathematics
SUMMARY POINTs
� 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
Solutions of Chapter 13
170
SE Production Limited