Final answer:
The bounded area is calculated by integrating the function y = x^3 - 10x^2 + 27x - 18 between its roots, but without the roots or a solved equation, the area cannot be determined from the given options.
Step-by-step explanation:
The area bounded by the curve y = x^3 - 10x^2 + 27x - 18 and the x-axis (y=0) can be found by integrating the function with respect to x. To find the points of intersection, we set y to zero and solve for x, yielding the bounds of integration. The definite integral of the given function from the lower to the upper bound provides the total area under the curve, which will be the bounded area.
- First, we find the roots of the cubic equation to determine the bounds of integration.
- Next, we perform the definite integral of the function between these bounds.
- Finally, we calculate the exact value of this integral to find the area.
Unfortunately, without further information such as the specific bounds of integration or a means to solve the cubic equation provided, we cannot determine the exact area. Therefore, we cannot confidently choose between options A) 42 square units, B) 36 square units, C) 54 square units, or D) 48 square units.