
(ii) The area bounded by the curve x = f (y)
y = axis and the abscissae at y = c and y = d is given by

Note 1:
The area bounded by the curves f(x) and g(x) and the ordinates x = a and x = b is given by


Note 2:
If curve f (x) lies above the x-axis and g (x) lies below the x-axis then area bounded by f (x) and g (x) is


Note 3:
If f (a) and f (b) are opposite in sign then the curve crosses the x-axis say at c.
Then the area bounded the curve f (x), x-axis and the ordinates x = a and x = b is

Example:
Find the area of the region between the X-axis and the graph of f(x) = x3 - x2 - 2x -1 ≤ x < 2.
Solution:
Let us find the values of x in the given interval, for which
f(x) = 0x3 - x2 - 2x = 0
x(x2 - x - 2) = 0
Partition the domain [-1, 2] to subintervals [-1, 0] and [0, 2]




