Did I do it right?Or I'm miss-interpreting the question?I'm so confused!!

Hi all, I'm trying to Write a program to calculate the volume under x^2 +1 curve when the curve is rotated around the x axis. The Integration of x from 0 to 3 with an increment of 0.1 using the disk method.Then Add to the above program, saving each value of the integral as well as the x coordinates in arrays, and plotting them to show the change in volume (of the revolution) as x goes from 0 to 3.0.We didn't have integration on MATlab class yet so I used the method:

l = 0.1;

for index = 1:30;

    x(index) = (index-1)*0.1;

    y1(index) = pi*((x(index).^2 +1)^2)*l;

    y2(index) = (-pi*((x(index).^2 +1)^2)*l);

end

%PLOT x VERSUS y

plot(x,y1,'m*-',x,y2,'b^--');

However,I'm not confident with my approach.If I just do y1,erasing y2,I get a graph of a simple curve,which doesn't represent any 'change of volume' asked by original question.That's why I used y2 as a function of y1,but the negative one,which goes on the -y coordinate,just to make it analogous with the disk method of integration rotating around x axis.I'm very confused!I'm not sure if that's what 'the change of volume' asks.Or should I think about graphing in three dimension?If so then how do I do that?

Answer 1

[John D'Errico]

So, for ANY value of x, if that curve is rotated around the x axis, then what is the radius of the circular cross section?

deltax = 0.1;
x = 0:deltax:3;
radius_x = x.^2 + 1;

The area of that disk is what?

area_x = pi*radius_x.^2;

We can compute a cumulative volume, where that integral is defined by the rectangle rule simply using cumsum.

volume_rect = cumsum(area_x*deltax);

Of course, we could have used a cumulative trapezoidal rule, so cumtrapz.

If you MUST avoid those tools, then a simple loop will suffice, accumulating that integral. I'm not sure what it is you know, and what you are allowed to use, so you need to decide.

[Mobasher Hossain]

I got the volume right using sum=o;sum=sum+increment method but your's one also gives the same volume.However, I'm asking about how to plot y's for each x the shows 'the volume change' in 2d plotting or 3d plotting,maybe.My confusion is there.I just don't know how can I show the change in the volume as I rotate it.I explained my concern, and confusion with my own plotting approach at the bottom of the original question.I'd really appreciate your help.

[John D'Errico]

The volume "change" as you rotate it? What are you rotating? I think you are getting confused.

The volume computed is that of the surface of rotation. You have implicitly rotated that curve into a surface by computing the area of each circular disk.

If you want to compute the differential volume along the x axis,

diff(volume_rect)

does that. This is the change in volume as we move along the x axis. Note that there is one less element in that vector, since it is a difference.

In fact, this is exactly what was requested:

"show the change in volume (of the revolution) as x goes from 0 to 3.0."

The revolution refers to the surface of revolution. The change in volume merely asks to see how that volume changes as we move along the x axis.

[Mobasher Hossain]

I got your point......sorry I was confused.....thanks!!