Example 1 :
Evaluate over the region enclosed by and .
The region of integration is shown in the figure
Example 2 :
Evaluate the integral over the region bounded by the lines y = x, y = x – 1, y = 0 and y = 1.
The region of integration is shown in figure. It is easier to evaluate the integral first w.r.t. x and then w.r.t. y.
Example 3 :
Evaluate over the region bounded by xy = 1, y = 0, y = x and x = 2.
The region of integration is as shown in figure. It has to be partitioned by line x = 1, before integration first w.r.t. y and then w.r.t x,