Use cylindrical shells to find the volume of the solid when the region enclosed by y = x², x = 2, x = 4, y = 0 is revolved about the line x = 2. A) 45.333 $\pi$ B) 22.667 $\pi$ C) 330.667 $\pi$ D) 11.333 $\pi$ E) 2.011 $\pi$

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The correct answer is A because the volume of the solid is found by integrating the area of the cross-sections of the solid with respect to the axis of revolution. The cross-sections are circles with radii equal to the distance from the axis of revolution to the curve y = x^2, which is 2 - x. The height of the cross-sections is the length of the curve y = x^2 between x = 2 and x = 4, which is 4 - 2 = 2. Therefore, the volume of the solid is:V = ∫[2,4] π(2 - x)^2 dx = π∫[2,4] (4 - 4x + x^2) dx = π[4x - 2x^2 + (1/3)x^3]_[2,4] = π(45.333)

Use Cylindrical Shells to Find the Volume of the Solid π\piπ

Use Cylindrical Shells to Find the Volume of the Solid $\pi$