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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.8, Problem 112E

To determine

**To calculate: **The area common to the regions formed by the inequalities

Expert Solution

The area of the region is

**Given information:**

The inequalities

**Formula used:**

The standard form of the equation of the circle is

**Calculation:**

Consider the provided inequalities

Rewrite the inequality

And

Recall that the standard form of the equation of the circle is

Compare,

Therefore, inequality is a circle with center at

Now, the inequality contains all point

Also,

Red shaded region represents

Now, the region common to the inequalities is shaded by green color which is a sector with included angle as

The area of circular sector is expressed as

Substitute r as 3 and

Thus, the area of the region is