Area Of The Region Bounded

To find the area of the region bounded by , , , and the x-axis, we start by expressing in terms of from the equation :

The area between and under the line is given by:

Evaluating this integral:

Therefore, the area of the region is 16 sq units.

The equation of the line is:

Rewriting:

To find the intercepts:

1. When , .
2. When , .

The lines and , together with , form a triangle with vertices:

The area of the triangle is:

where the base is and the height is :

Simplify:

Thus, the area of the region is: