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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = 8×3, y = 0, x?

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Dr. Juanita Wolff

Feb 20, 2025

use [ 2π radius height thickness ] concepts…..radius is [ 2 – x ] , x in [ 0 , 1 ] , height is [ 8 x³ – 0 ] , thickness is [ dx ] …trivial integration... Show More
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Dr. Juanita Wolff

Feb 20, 2025

y=8x^3x^3=y/8x = y^(1/3) /8^(1/3) x = y^(1/3) /2x=1y^(1/3) /2 = 1y^(1/3) = 2y = 2^3 = 8y=0Volume = pi ∫ [0,8] ((2 -y^(1/3) /2)^2 – (2-1)^2 ) dyVolume = (pi/4) ∫ [0,8] y^(2/3) -8y^(1/3) +12) dy= 24pi/5... Show More
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