Question

Find the volume of the infinitely long horn that is generated by rotating
the region bounded by y = 1
x and y = 0 and lying to the right of x = 1 about the
x-axis. where to start just give me a hint.

Answer 1

hey there
im working on another problem.
can you follow me.

Answer 2

well the student isnt responding, ok

Answer 3

i know i need to write an integration for the disc formed by roation but i don't know how

Answer 4

waityour problem doesnt make sense

Answer 5

it says bounded by x =0, y=0, y=1 , x=1 , then to the right of x=1 ?

Answer 6

Find the volume of the infinitely long horn that is generated by rotating
the region bounded by y = 1/x and y = 0 and lying to the right of x = 1 about the
x-axis. sorry for the error

Answer 7

ok

Answer 8

ok so integral pi (1/x)^2 from 1 to infinity

Answer 9

ohk so the infinity part just means that upper limit is infinity :)

Answer 10

so you get -pi x^-1 from 1 to infinity,

Answer 11

so -pi / infinity - ( - pi / 1) = 0 + pi = pi

Answer 12

thanks :)

Answer 13

make me fan

Answer 14

already did :)

Answer 15

:)

Answer 16

so whats interesting about this, there is no bottom to this horn, so water can travel infinitely, but , the volume is finite?

Answer 17

i mean if you think of the volume as being submerged in water, you would think, ok , how can this "water bottle horn" have pi units of water