Final answer:
To find the volume of the solid obtained by rotating the region under the graph of the function f(x)=3x−x² about the x-axis over the interval [0,3], we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region under the graph of the function f(x)=3x−x² about the x-axis over the interval [0,3], we can use the method of cylindrical shells.
The volume can be calculated using the formula V = ∫(2πxf(x)) dx, where x represents the variable of integration and f(x) is the function representing the height at each x-value. In this case, f(x) = 3x - x².
Therefore, the volume of the solid is V = ∫(2πx(3x - x²)) dx over the interval [0,3]. We can solve this definite integral to find the exact value of the volume.