Final Answer:
The total shaded region of x √(4 - x²) from -2 to 2 can be found using the Disk Method (option A).
Step-by-step explanation:
To determine the total shaded region, we employ the Disk Method, as this geometric shape is best suited for the given function x √(4 - x²). The formula for the Disk Method involves integrating the area of each infinitesimally thin disk along the interval from -2 to 2. The integral is expressed as ∫₋₂² π f(x)² dx, where f(x) represents the radius of each disk (option A).
The function x √(4 - x²) can be visualized as a semi-circle in each quadrant, and by squaring the function, we obtain the radius of the disks. The integral becomes ∫₋₂² π (x √(4 - x²))² dx. The limits of integration, -2 to 2, cover the entire region of interest.
By carefully evaluating this integral, we can determine the total shaded region using the Disk Method. This method is appropriate when the function is revolved around the x-axis, creating disks perpendicular to the axis. It provides a precise way to calculate the area enclosed by the curve and the x-axis within the specified interval.