Final answer:
To find the bounded area between curves f(x) and g(x), we solve for their points of intersection and integrate the difference between them over that interval.
Step-by-step explanation:
The task is to find the area of the region bounded above by the curve f(x) = √[4]{x} and g(x) = 2 - x, and bounded below by the x-axis. To find this area, we first need to determine the points of intersection of the curves f(x) and g(x), which are the limits of integration. These points can be found by setting f(x) equal to g(x): √[4]{x} = 2 - x.
Once the points of intersection are found, the area can be calculated by integrating the difference between the higher and lower curves, from the leftmost to the rightmost points of intersection. This means we will evaluate the integral of (2 - x) - √[4]{x} within the intersection points.
Since this is a high school mathematics problem, the use of calculus and understanding the graphical representation of the problem is expected. Drawing the curves and shading the area of interest provides a visual aid in understanding the problem. Once the definite integral is evaluated, we obtain the area of the bounded region.