Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x y=0 x=2 and x=4 about the line x=1

Answer 1

OK, this can be expressed as an integral. Give me a moment.

Answer 2

That's not it. It's being rotated around x=1.

Answer 3

Ahh, didn't see that, thanks

Answer 4

Here goes...

Answer 5

I have that graph, but i just dont know what else or how to set it up correctly :(

Answer 6

\[V=\pi r^{2}\]

Answer 7

Now we need to get a function for r and integrate it.

Answer 8

so its in terms of 0 to 4. ?

Answer 9

\[r=x-1\]

Answer 10

I'd do in terms of y I think:
\[pi*\int\limits_{0}^{4}y^2-2^2\]
Right? Probably messed something up there
And yes, if you do in terms of y you'd go from 0 to 4. Fixed something in the integral. It's too late, lol.

Answer 11

i get confused when to use x or y in the shell method? So although it asks for disks/washers, i can use Shells?

Answer 12

That equation above there is washers, pi*r^2 - pi*r^2, outer disk minus inner disk, that's a washer.

Answer 13

still doesn't help, i know that but what is the outer and what is the inner?

Answer 14

Lemme see if I can draw this for you, maybe we can make some sense of it.

Answer 15

So we'll make a small slice horizontally like this, and spin it around x=1.