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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].

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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.

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