Let Vx and Vy be the volumes of the solids that result when the region enclosed by y=1/x y=0 x=1/2 and x=1/2 (b 1/2) is revolved about the x-axis and the y-axis, respectively. Is there a value of b for which Vx = Vy?

Question

Let Vx and Vy be the volumes of the solids that result when the region enclosed by y=1/x y=0 x=1/2 and x=1/2 (b > 1/2) is revolved about the x-axis and the y-axis, respectively. Is there a value of b for which Vx = Vy?

anonymous · Answer

@sourwing i accidentally closed my question. would you be able to help ? :/

anonymous · Answer

well, you see, the question doesn't ask for what it is. It's yes/no question :DDD

anonymous · Answer

@sourwing  hehe i wish it was as simple as that! the answer manual actually gives an actual number so I think i have to support the yes

anonymous · Answer

you have the solution manual and still don't know the answer? O.O

anonymous · Answer

Well Idk how they got the answer it only give me the answer

anonymous · Answer

@sourwing

anonymous · Answer

attachment

anonymous · Answer

it's revolved around the x-axis, what is you setup?

anonymous · Answer

well this is where I have my doubts. Im not sure where to start!

anonymous · Answer

V_x = pi ∫ radius^2 [disk method]
V_x = pi ∫(1/x)^2 dx, from 1/2 to b

around the y-axis:
V_y = 2pi ∫(radius) (height) [shell method]
V_y = 2pi ∫ x (1/x) dx from 1/2 to b

anonymous · Answer

set V_x = V_y and solve for b

anonymous · Answer

oh thank you! let me try it out

anonymous · Answer

for Vx I got..$$2\pi \left( \frac{ 4b ^{2}-1 }{ b ^{2} } \right)$$

anonymous · Answer

and my Vy=2pi

anonymous · Answer

wait for the Vx just pi not 2pi!

dan815 · Answer

can you exaplain ur question to me

dan815 · Answer

why are there 2, x=1/2s

anonymous · Answer

oops I'm sorry i may have wrote that twice it is supposed to say…

dan815 · Answer

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