Find-the-volume-of-the-solid-generated-when-the-region-enclosed-by-y-x-y-0-and-x-9-about-the-line-x-9-

Question Number 26162 by lizan 123 last updated on 21/Dec/17

F i n d t h e v o l u m e o f t h e s o l i d g e n e r a t e d w h e n t h e r e g i o n e n c l o s e d

b y y = \sqrt{x}

y = 0 a n d x = 9 a b o u t t h e l i n e x = 9

Answered by ajfour last updated on 21/Dec/17

Commented by ajfour last updated on 22/Dec/17

V o l u m e = \int_{0}^{3} π {(9 - x)}^{2} d y

= π \int_{0}^{3} {(9 - y^{2})}^{2} d y

= π (81 y - \frac{18 y^{3}}{3} + \frac{y^{5}}{5}) ∣_{0}^{3}

= π (9 \times 27 - 6 \times 27 + \frac{9}{5} \times 27)

= π (\frac{24 \times 27}{5}) = \frac{648 π}{5} s q . u n i t s

Commented by mrW1 last updated on 22/Dec/17

o r :

V = \int_{0}^{9} 2 π (9 - x) y d x = 2 π \int_{0}^{9} \sqrt{x} (9 - x) d x

= 2 π {[6 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}}]}_{0}^{9}

= 2 π [6 \times 9^{\frac{3}{2}} - \frac{2}{5} \times 9^{\frac{5}{2}}]

= 2 π [\frac{12}{5}] \times 27

= \frac{648 π}{5}

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