use-cylindrical-shells-to-find-volume-y-x-3-y-8-about-x-9-

Question Number 136910 by leena12345 last updated on 27/Mar/21

u s e - c y l i n d r i c a l - s h e l l s - t o - f i n d - v o l u m e

y = x^{3} / y = 8 / a b o u t - x = 9

Answered by liberty last updated on 27/Mar/21

Vol = 2 π \int_{0}^{8} (8 - x) x^{3} dx

= 2 π \int_{0}^{8} ({8 x}^{3} - x^{4}) dx

= 2 π {[{2 x}^{4} - \frac{x^{5}}{5}]}_{0}^{8}

= 2 π {(x^{4} (2 - \frac{x}{5})]}_{0}^{8}

= 2 π . 8^{4} . \frac{2}{5} = \frac{4 π . 8^{4}}{5} = \frac{16, 384 π}{5}

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