Hi, I’m pretty new using the Washer and Shell’s method.
So far I don’t really know much of the distinction between the two.
This is what I know that both of them requires:
Each one requires an outer radius and inner radius.
The only way I know how to find the outer radius and inner radius is by graphing them, and see where the points intersect, and make a cone out of them. Sometimes whenever I know the curve goes like the other way, I instantly know it’s an inner radius. What I mean is, like if I had x2 and √x, then x2 is the inner radius because it goes outward, so it doesn’t make like a round semi-circle. Am I right?
Though sometimes I get confused by the y=0 part, where it’s mainly just a line, so I’m not really sure how to make the shape. If anyone can give me some tips, or know other ways of telling the outer and inner radius, let me know.
After finding the outer and inner radius, I believe using the Washer and Shell’s method both get you the same answer, right?.
Also, when it revolves around the x-axis, you would set both of the inner and outer radius equal to 'x' right? And if it was revolving around y, then it would be set equal to 'y'?
Like for example: x+y2=9, x=0. So I would set this up using the Shell method by doing the equation above, but I will make the first function equal to x like this: x=9-y2, right?.
This is what I know about the Washer’s:
The equation is πR2w. So I would use that, and subtract it from the inner radius, πr2w.
So it would be like π∫R2-r2, then just plug in the radius, integrate it, and plug in the ‘b’ and ‘a’ and subtract the ‘a’ from ‘b’ right? That’s all it is to the Washer method?
This is what I know about the Shell’s:
It’s almost the same as the Washer’s except…
It’s like this: 2π∫x(R-r)
Then plug in the inner and outer radius, and then integrate, and plug in the ‘b’ and ‘a’ and subtract the ‘a’ from ‘b’ right? I’m not really sure about the Shell method the most, since it has the 2π on the outside, and an x on the inside for every equation?
If anyone know an easy way to study the Washer, and Shell, or give me some tips, please let me know! J