8.
3 Integration of
TIP
WORKED EXAMPLE 8.3
Find .
Answer
Write .
TIP
can be written as or . Do
not confuse with .
EXERCISE 8C
1 Work out the following integrals.
f
2 Evaluate each of the following integrals, giving your answer in an exact form.
3 Show that where is an integer to be found.
PS 4 Calculate the area of the shaded region in the graph represented by
, where B is the intersection of the graph with the
-axis. Give your answer as an exact value in the form .
PS 5 Show that , where and are integers to
be found.
6 a Find the area of the region enclosed by the curve with equation , the -
axis and the lines and .
b Find the volume generated when this area is rotated about the -axis.