why dosen't out put as short answer?

syms y
R1=(nthroot(y-2,3)+2);
R2=y;
R3=1;
eq1=int(R1^2,y,1,2.1);
eq2=int(R2^2,y,2.094,4);
eq3=int(R3^2,y,0,1);
format short 
volume=(eq1+eq2+eq3)*pi

volume = 

Answer 1

[Star Strider]

Because it is symbolic, not numeric.

To get a numeric result use either vpa or double —

syms y
R1=(nthroot(y-2,3)+2);
R2=y;
R3=1;
eq1=int(R1^2,y,1,2.1);
eq2=int(R2^2,y,2.094,4);
eq3=int(R3^2,y,0,1);
format short 
volume=(eq1+eq2+eq3)*pi

volume = 

vpa_volume = vpa(volume)

vpa_volume = 

67.308283557712918056555924159997

double_volume = double(volume)

double_volume = 67.3083

If you want to always have this sort of result, see the documentation on sympref, and specifically Display Symbolic Results in Floating-Point Format.

.

[Walter Roberson]

The purpose of solve() and int() are to return indefinitely precise answers whenever possible. solve() avoids approximate numeric solutions, and int() never uses approximate numeric solutions. If you int() and the exact theoretical solution is then int() will return that, not 1.236<something>

If what you want is a numeric approximation then you should be reconsidering whether you should be using int() at all: perhaps you should be using the pure-numeric integral() or perhaps you should be doing extended precision numeric approximation using vpaintegral()