Question

Find the volume of the solid obtained when the region bounded by the line y=2x, x=3 and the x-axis is rotated about the y-axis

Answer 1

draw a picture...

Answer 2

what will be the bounds on the integral?

Answer 3

actually better Q: what method do you want to use. Washer or shell?

Answer 4

shell and 0 and 6?

Answer 5

actually I don't care which method, I am confused by everything in general

Answer 6

Is it a cylinder less a cone?

Answer 7

shell is a good choice

Answer 8

so what will be the bounds if we do shell method?

Answer 9

0-6?

Answer 10

in shell method we integrate along the radii of the shells

Answer 11

that means we integrate along x in this case
what are the bounds on x?

Answer 12

0-3?

Answer 13

I have no idea

Answer 14

yes it is 0-3

Answer 15

now look at my other picture with a cylinder drawn in
what is the height of each cylinder?

Answer 16

h=?

Answer 17

2

Answer 18

why do you think that?

Answer 19

or is that 6 now

Answer 20

it's not a number, it's an expression
I am asking you what the height of each cylinder is
look at the picture: it is the top function minus the bottom (which is just the x axis)