**Example 1 :**

Evaluate over the region enclosed by and .

**Solution :**

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.

**Solution :**

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.

**Solution :**

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,

So,

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