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anonymous
 one year ago
Find the volume of the solid that results when the region bounded by y=0, x=0, x=1, and y=x^2+1 is revolved around the yaxis using discs/washers.
anonymous
 one year ago
Find the volume of the solid that results when the region bounded by y=0, x=0, x=1, and y=x^2+1 is revolved around the yaxis using discs/washers.

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0"...using discs/washers" it's way easier just using calculus have you had a go?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know how to use disks/washers for most problems, but after I graphed this one, I couldn't figure it the equation. It's wrong, but I did this : \[\pi \int\limits_{0}^{2}(\sqrt{y1}^2(0)^2dy\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Hmm :) Ya if we look at the graph...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1444636132588:dwNotice that down here, your left boundary is NOT the function x!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2So when you're doing this problem, where the boundaries change, you want to split it into two separate integrals.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1444636317000:dwI guess you don't really need an integral for this lower part here.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Spin it around,dw:1444636360587:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2volume of that cylinder = (surface area)(height)\[\large\rm v=(\pi\cdot1^2)(1)=\pi\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2And your integral looks a little goofed up.. hmmm thinking...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1444636534244:dwSo we've figured out this bottom section here. Let's take a slice vertically of this upper region with "thickness" dy.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2We get a washer, which is a disk with a hole in it. So you have the right idea there. But you're subtracting incorrectly. Hmm, let's see if we can fix that.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1444636696922:dwThis will be our \(\large\rm \color{blue}{R}\) and \(\large\rm \color{red}{r}\).