Find the area of the region in the first quadrant enclosed by the y-axis, the line `y=x` and the circle `x^2+y^2=32 ,` using integration.

Explanation

To find the area of the region in the first quadrant enclosed by the y-axis, the line \( y = x \), and the circle \( x^2 + y^2 = 32 \), we can follow these steps:

### Step 1: Identify the curves and their intersection points
The curves involved are:
1. The line \( y = x \)
2. The circle \( x^2 + y^2 = 32 \)

To find the points of intersection, we substitute \( y = x \) into the equation of the circle:
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