definite integral not giving exact answer

Hi,

I have a triple integral with the following code:

inner_int=int(r*sin(phi),phi,[acos(4/5) pi-acos(4/5)])
middle_int=int(inner_int,r,3,5)
Mass_S=int(middle_int,theta,0,2*pi)

The answer I get from the first line is

-r*(cos(175787564848171/70368744177664) - cos(181129459610871/281474976710656))

When it should be 8/5*r

I have tried adding 'IgnoreAnalyticConstraints',true to the end of int but it didn't work. Is there anything I can do to get MATLAB to compute this as an exact solution. For reference the shape to be integrated is a sphere with a cylindircal hole drilled in it and spherical coordinates are required. Thanks

Answer 1

[Steven Lord]

Compute your limits of integration symbolically to avoid roundoff error.

f = sym(4)/5;
a = acos(f);
inner_int = int(r*sin(phi), phi, [a, pi-a])

[AgentWindu]

Great

Thanks for your help, this worked

Answer 2

[Cameron B]

I don't know what the issue is. I did this and got 8*r/5. The answer seems to be correct.

syms r
sym(-r*(cos(175787564848171/70368744177664) - cos(181129459610871/281474976710656)))