Area Under Simple Curves

To find the area of the region bounded by the curve and the x-axis, we need to recognize that this curve represents the upper semicircle of a circle centered at the origin with radius 7 (since is the equation of a circle of radius 7).
Steps to solve:

1. Equation of the semicircle:
This is the upper semicircle of a circle with radius centered at the origin.

2. Limits of integration:
The semicircle extends from to .

3. Area of the semicircle:
The area of a full circle with radius is given by:

Since the radius is 7:


4. Area of the upper semicircle:
The area of the upper semicircle is half of the area of the full circle:


Final Result:
The area of the region bounded by the curve and the x-axis is:

Hence, the correct option is:
(B) 49 π/2 sq. units