Integrating and graphing in 3

Hello, I am fairly new to matlab, but it would be a great help if someone could answer the following question. I would like to revolve a function around the x axis and then graph it in 3D using matlab. The function is as follows:

   f(x)= (((6.4)/(x+12))*sin((2pi)/6.5x)+3)

The function to revolve it around the x-axis, I believe is:

 V=∫ pi[f(x)]^2 dx

The domain I wish to graph it between is:

0≤x≤16

I know, that using the cylinder function, it can be revolved but I am unsure as to how to first integrate this function using the above formula, then graph it in 3D in between the desired domain. That is somehow, involving x,y,z.

Help would be great to somehow integrate the function using the V formula, then using the cylinder function, graph it in 3D between the domain.

Thanks!

Answer 1

[Star Strider]

You can integrate it with the Symbolic Math Toolbox.

The plot is not very interesting:

syms x 
f(x) = (((6.4)/(x+12))*sin((2*pi)/6.5*x)+3);
intf(x) = int(f, x);
intf(x) = simplify(intf, 'Steps', 20);
f_int = matlabFunction(intf)

figure(1)
fplot(intf, [0 16])

Anonymous function:

f_int = @(x)x.*3.0-exp(pi.*3.076923076923077e-1i).*ei(pi.*(x+1.2e1).*3.076923076923077e-1i).*3.2i+exp(pi.*1.923076923076923e-1i).*ei(pi.*(x+1.2e1).*-3.076923076923077e-1i).*(1.6e1./5.0)