Here's the question you clicked on:
rainbow22
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
Do you know about multivariable calculus perhaps? Or do you want the easy-not-understanding-what-you're-doing way
No, I am supposed to use the Disk Washer method. I can do it with antiderive(2-y) 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.
There's a hole in the solid.. so it's called Washer Method.
So how does this method work?
I do antiderivative from a-b in terms of x or y (y in this case because I rotate about y axis) pi (outer radius)^2 - (inner radius)^2
\[\int\limits_{a}^{b} \pi (outer radius)^2 -(innerradius)^2 dx\]
I don't how that works, I'm afraid.
|dw:1359838561883:dw|So let's look at one slice.
Oh you're doing the washer/disk method, my mistake.. Lemme slice that differently.
|dw:1359838731527:dw|Ok this type of slice will give us a Disk.
|dw:1359838764034:dw|So we want to get the Volume of this disk.
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)
\[\large y=x^2 \qquad \rightarrow \qquad x=\sqrt y\]
\[\large V=\pi\left[(2)^2-(\sqrt y)^2\right]dy\]
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?
Simplifying things down gives us, \[\large \pi \int\limits_0^4 4-y \;dy\]
Imma check my work real quick to make sure I didn't make a mistake somewhere. A little tired, it's possible. lol
Yah I think that's right. Confused about any of that? I went through it a little sloppy D:
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!