In this example, we're going to use the Method of Cylindrical Shells to find the volume of the solid of rotation that we discussed in the previous lecture.
@@whitecraneeducation2228 yea...just take a sample element dv , which has a volume of 2*pi*x*f(x)*dx. integrate using the same limits and we get the same result, rather than substracting the larger volume from smaller one and simplifying it, i think its more easy to visualize a small volume element and finding its volume using basic geometry.
@@bharathharish9905 Were you referring to this video or the one where I derived the formula? There wasn't any mention of inner versus outer radii here - I just went straight to the formula. In the other video, I can see how someone could jump to that formula based on what they've seen previously but relying on your intuition, especially for students who are relatively new to the material, is a risky choice. It's better to start with the definitions or theorems you've already derived and go forward from there. That's what I was trying to do in that lecture.
bro there are better intuitive explanation (for cylindrical shell)for the entire answer.dont make math more complicated than it is...
This was a pretty straightforward application of the formula. If you've got another approach, we'd love to hear it.
@@whitecraneeducation2228 yea...just take a sample element dv , which has a volume of 2*pi*x*f(x)*dx. integrate using the same limits and we get the same result, rather than substracting the larger volume from smaller one and simplifying it, i think its more easy to visualize a small volume element and finding its volume using basic geometry.
@@bharathharish9905 Were you referring to this video or the one where I derived the formula? There wasn't any mention of inner versus outer radii here - I just went straight to the formula.
In the other video, I can see how someone could jump to that formula based on what they've seen previously but relying on your intuition, especially for students who are relatively new to the material, is a risky choice. It's better to start with the definitions or theorems you've already derived and go forward from there. That's what I was trying to do in that lecture.