## anonymous one year ago Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?

1. anonymous
2. anonymous

@jim_thompson5910 @zepdrix Appreciate it if you guys could give me a hand.

3. zepdrix

Oh we only have to set it up this time? Nice!

4. zepdrix

|dw:1444441768757:dw|

5. zepdrix

|dw:1444441990320:dw|Given these boundary lines, do you understand which region we're dealing with?

6. anonymous

|dw:1444442057843:dw|

7. zepdrix

Ok good good good. That's the one surrounded by all of our boundaries.

8. zepdrix

OH NOES! :( I just realized.. they have all of the options in terms of y. UGHHHH

9. zepdrix

They set up the integral in terms of y. So we need to actually slice the other direction. Lemme erase all this garbage a sec :c

10. zepdrix

|dw:1444442601942:dw|So instead we'll get a disk :d

11. anonymous

I would've never noticed that lol. Good eye

12. zepdrix

$\large\rm y=x^3\qquad\to\qquad x=y^{1/3}$Here is how we can think of our curve in terms of y instead of x.

13. zepdrix

|dw:1444442739693:dw|So again, our radius is this blue minus red