Struggling with integration.

How would I integrate this equation in matlab? V=∫pi*(R1+R2-sqrt(R2^2-x^2))^2 dx with limits -0.5D and 0.5D.

I have V, R2, and a height, D.

R1 is an unknown which I have to solve for.

What I've tried so far.

syms r1 r2 d x;

f= (pi()*(r1+r2-sqrt(r2^2-x^2))^2)

F = int(f, x)

G= int(F,r2)

a=int(F, x,0.5,-0.5)

[John D'Errico]

Why have you written a DOUBLE integration, when your question shows a single integral?

[Przemyslaw Trzybinski]

I saw a post when I was searching for a solution, where someone also had a single integration, but was advised to first calculate undefinite integral using variable y (in his case).

And then integrate again using x.

So would I simply use

syms x r1 r2

f= (pi()*(r1+r2-sqrt(r2^2-x^2))^2)

F = int(f, x, -0.5,0.5) ?

Answer 1

[Divija Aleti]

Hi,

I understand that you have the values of 'R2', 'V' and 'D', and you have to solve the equation, 'V=∫pi*(R1+R2-sqrt(R2^2-x^2))^2 dx' to find the value of 'R1'.

Take a look at the following code which shows how to solve for 'R1'. The values of 'R2', 'V' and 'D' are assumptions I made.

syms x R1
R2=3;
D=4;
V=25;
f = pi*(R1+R2-sqrt(R2^2-x^2))^2;
fint = int(f,x,[-0.5*D 0.5*D]);
eqn=V-fint==0;
sol_R1=vpa(solve(eqn,R1));

For additional information on the functions used, have a look at the following links:

https://www.mathworks.com/help/symbolic/int.html#btyb52x-1

https://www.mathworks.com/help/symbolic/solve.html

https://www.mathworks.com/help/symbolic/vpa.html