Integration with pi - Rational Approximation?

Question

0 개 추천

I'm having trouble understanding the difference between these two integration commands:

clear; syms y;
int(1000*9.8*(10-y)*(pi*6^2),0,10)
int(9.8*1000*(pi*6^2)*(10-y),0,10)

On my machine (2019b - Windows) and MATLAB Online, using format short I get:

ans =

17640000*pi

ans =

14876074069235525/268435456

I often receive odd rational approximations when integrating using pi (note that leaving pi out of the integral fixes the issue). I haven't been able to find an answer as to why this happens. I'm assuming MATLAB computes a decimal answer using pi, cuts the approximation at the 14 or 15th decimal place, then creates a fraction out of the result, but why does this happen some times and not others?