Sketch the region common to the circle `x^2 +y^2=16` and the parabola `x^2=6y` Also find the area of the region using intergration

Explanation

To solve the problem, we need to sketch the region common to the circle \( x^2 + y^2 = 16 \) and the parabola \( x^2 = 6y \), and then find the area of that region using integration. Let's go through the steps systematically.

### Step 1: Identify the Circle and Parabola
The equation of the circle is:
\[ x^2 + y^2 = 16 \]
This is a circle centered at the origin (0, 0) with a radius of 4.
...