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rainbow22
 3 years 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
rainbow22
 3 years 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

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Thomas9
 3 years ago
Best ResponseYou've already chosen the best response.0Do you know about multivariable calculus perhaps? Or do you want the easynotunderstandingwhatyou'redoing way

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0No, 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.

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0There's a hole in the solid.. so it's called Washer Method.

Thomas9
 3 years ago
Best ResponseYou've already chosen the best response.0So how does this method work?

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0I 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

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{a}^{b} \pi (outer radius)^2 (innerradius)^2 dx\]

Thomas9
 3 years ago
Best ResponseYou've already chosen the best response.0I don't how that works, I'm afraid.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1359838561883:dwSo let's look at one slice.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Oh you're doing the washer/disk method, my mistake.. Lemme slice that differently.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1359838731527:dwOk this type of slice will give us a Disk.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1359838764034:dwSo we want to get the Volume of this disk.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1The 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)

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1\[\large y=x^2 \qquad \rightarrow \qquad x=\sqrt y\]

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1\[\large V=\pi\left[(2)^2(\sqrt y)^2\right]dy\]

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Then 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?

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

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

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

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0It'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!
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