Question

Let R be the region of the plane bounded by the curves y = 2x and 6x − y = 8. The region R is rotated around the y-axis. Use the washer method to find an integral
whose value is the volume of the solid that you get.

Answer 1

Also assume bounded by x-axis?

Answer 2

yes i think...please help

Answer 3

I'm trying to remember difference between washer method, shell method, disk method, but either way, I think I would integrate along the y-axis using the area of the washer as
\[\frac{y+8}{6} \space -\frac{y}{2}\]

Answer 4

integrate that with a dy from 0 to 4. I think that ought to do the trick.

Answer 5

Oh, sorry, I forgot the πr^2 business...

Answer 6

why is it y+8/6 - y/2

Answer 7

Just a sec, forgot to square the radii...

Answer 8

I solved the equations for x instead of y, so I could integrate along the y-axis using dy instead of dx.

Answer 9

I think that's what makes the washer shape instead of the shells shape, but I sometimes get those terms mixed up.

Answer 10

Ok, sorry, the area of each washer is
\[\left(\frac{y+8}{6} \right)^2 - \left(\frac{y}{2} \right)^2\]

Answer 11

It helps if you graph the lines to see which is the outer radius and which is the inner radius.
(If you haven't already)

Answer 12

so can you please draw all the stuff so i know where to start

Answer 13

Sure, I'll have to do it quick 'cause I'm about to leave to go to dinner.

Answer 14

but i need all the work too...

Answer 15

You're going to have to do some of this work on your own . . .

Answer 16

aw :(

Answer 17

i can't