Final answer:
To find the area of the region bounded by the given curve and line, you need to find the points of intersection, and then integrate the difference between the two functions over the interval determined by these points.
Step-by-step explanation:
The area of the region bounded above by the curve f(x) = (x - 9)²2 and the line g(x) = 15 - x, and bounded below by the x-axis can be found by calculating the area between the two curves.
To do this, we need to find the x-values where the curve and the line intersect. Set f(x) = g(x) and solve for x:
(x - 9)²2 = 15 - x
To find the points of intersection, we need to solve this quadratic equation.
Once we find the points of intersection, we can calculate the area between the two curves by integrating the difference between the two functions over the interval determined by the points of intersection.