进行数值积分，在原积​分上乘一个小量（常量​）积分结果发生变化

进行数值积分；在原积分上乘一个小量，积分结果发生变化；或者是原积分很小1e-40这个量级，我怎么确定积分结果是正确的，求解答

Answer 1

[Suraj]

Greetings,

I understand that you're performing numerical integration and you're concerned about the accuracy of your results, especially when multiplying the integral by a small quantity or when the integral itself is very small (on the order of 1e-40).

If you're multiplying your integral by a small quantity and seeing a change in the result, this could be due to the precision of the numerical integration method. When dealing with very small numbers, precision can become an issue due to the limitations of machine precision.

Here are a few suggestions that you can try:

1. Increase the precision of your calculation: In MATLAB, you can use the "vpa" function for variable precision arithmetic. Please refer to the documentation for "vpa" function: https://www.mathworks.com/help/symbolic/vpa.html
2. Compare with analytical results if possible. If you can solve the integral analytically, you can compare the numerical result with the analytical result to check the accuracy.
3. Modify the error tolerance of “integral” function. You can learn more about this here: https://www.mathworks.com/help/matlab/ref/integral.html#btc_m8o-4

I hope this helps.

Best Regards,

Suraj.