the volume between y= x^2 y=18-x^2 x=0 and revolved around y=18 Solution shell m

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shell method: radius = x - 0 ====> x = 0 y = 3x^2 y = 18x - 6x^2 area or shell height = 18x - 6x^2 - 3x^2 ====> 18x - 9x^2 intersection: 3x^2 = 18x - 6x^2 3x^2 + 6x^2 - 18x = 0 9x^2 - 18x = 0 9x * (x - 2) = 0 ------> x = 0 & 2 2 ? 2 * p * x * (18x - 9x^2) dx 0 2 ? 2 * p * (18x^2 - 9x^3) dx 0 . . . . . . . . . . . . . . . .. . 2 2 * p * (6x^3 - (9/4)x^4) ] .. . . . . . . . . . .. . . . . 0 2 * p * (6 * (2^3 - 0^3) - (9/4) * (2^4 - 0^4) ) 2 * p * (6 * (8 - 0) - (9/4) * (16 - 0) ) 2 * p * (6 * (8) - (9/4) * (16) ) 2 * p * (48 - 36) 2 * p * (12) 24p

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