`y = x^2, y = 6x - 2x^2` Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.
The shell has the radius `x` , the cricumference is `2pi*x` and the height is `6x - 2x^2 - x^2` , hence, the volume can be evaluated, using the method of cylindrical shells, such that:
`V = 2pi*int_(x_1)^(x_2) x*(6x - 3x^2) dx`
(The entire section contains 134 words.)
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