To be honest, I'd probably do the inner integral (I assume that is on y) by hand, so we get that as:
(16 - 3*x^2 - z^2) - (x^2 + z*2) = 16 - 4*x^2 - 2*z^2
The other two integrals are as easy to write by hand too. So I'm not sure what the problem is here.
If you'd rather do it using syms, I'd split it up into three integrals to make it easier to read.
syms x y z
>> Iy = int(1,y,[x^2 + z^2,16-3*x^2-z^2])
Iy =
- 4*x^2 - 2*z^2 + 16
Given the limits of integration, I assume the middle integral must be on z, as the limits are a function of x. But you did write it as dy dx dz. Assuming the middle integral is on z, then you would write it as
Iz = int(Iy,z,[-sqrt(4-x^2),sqrt(4-x^2)])
You should do the rest. In the end, you should get a nice, round multiple of pi as the answer. But I don't want to do your homework for you.
