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find the volume of the solid formed by revolving the region bounded by y=x^2, y=0, and x=2 about the y axis
 one year ago
 one year ago
find the volume of the solid formed by revolving the region bounded by y=x^2, y=0, and x=2 about the y axis
 one year ago
 one year ago

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Thomas9Best ResponseYou've already chosen the best response.0
Do you know about multivariable calculus perhaps? Or do you want the easynotunderstandingwhatyou'redoing way
 one year ago

rainbow22Best ResponseYou've already chosen the best response.0
No, I am supposed to use the Disk Washer method. I can do it with antiderive(2y) to get the right answer but I'm pretty sure that's not following th formula I'm given which is outer radius minus inner radius.
 one year ago

rainbow22Best ResponseYou've already chosen the best response.0
There's a hole in the solid.. so it's called Washer Method.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.0
So how does this method work?
 one year ago

rainbow22Best ResponseYou've already chosen the best response.0
I do antiderivative from ab in terms of x or y (y in this case because I rotate about y axis) pi (outer radius)^2  (inner radius)^2
 one year ago

rainbow22Best ResponseYou've already chosen the best response.0
\[\int\limits_{a}^{b} \pi (outer radius)^2 (innerradius)^2 dx\]
 one year ago

Thomas9Best ResponseYou've already chosen the best response.0
I don't how that works, I'm afraid.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1359838561883:dwSo let's look at one slice.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Oh you're doing the washer/disk method, my mistake.. Lemme slice that differently.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1359838731527:dwOk this type of slice will give us a Disk.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1359838764034:dwSo we want to get the Volume of this disk.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
The outer radius appears to be the line x=2. And the inner radius our function which is in terms of x, we'll need it in terms of y to integrate since we sliced in the y direction (dy thickness)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large y=x^2 \qquad \rightarrow \qquad x=\sqrt y\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large V=\pi\left[(2)^2(\sqrt y)^2\right]dy\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Then to find the total volume in this enclosed area, we Integrate (add up all the slices) from one intersecting point to another. Where do they intersect? Ummm looks like.. y=0 and y=4?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Simplifying things down gives us, \[\large \pi \int\limits_0^4 4y \;dy\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Imma check my work real quick to make sure I didn't make a mistake somewhere. A little tired, it's possible. lol
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Yah I think that's right. Confused about any of that? I went through it a little sloppy D:
 one year ago

rainbow22Best ResponseYou've already chosen the best response.0
It's right. I realize what I did wrong! I had the wrong intersections/points. I did instead from 2 to 2.. not realizing that it was based on terms of y . thank you so much!
 one year ago
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