find-the-volume-of-the-region-between-curves-xy-4-and-x-y-5-revolvex-around-the-X-axis-

Question Number 91611 by ar247 last updated on 01/May/20

f i n d t h e v o l u m e o f t h e r e g i o n

b e t w e e n c u r v e s (x y = 4 a n d x + y = 5)

r e v o l v e x a r o u n d t h e X a x i s

Commented by john santu last updated on 02/May/20

v o l = π \int \underset{1}{\overset{4}{}} {(5 - x)}^{2} - {(4 x^{- 1})}^{2} d x

= π {[- \frac{1}{3} {(5 - x)}^{3} + \frac{16}{x}]}_{1}^{4}

= π [(4 - \frac{1}{3}) - (16 - \frac{64}{3})]

= π [\frac{11}{3} + \frac{16}{3}] = 9 π