![]() This is related to the Compiled -option-more about this below. Therefore, the time it takes to evaluate an integral is proportional to the number of MaxPoints and in some cases, the form of your function. Less important but still significant is the fact E (- (t/10)), which vanishes as t increases. Some properties of the integrand The dominant factor of the integrand is E (-50 2), which means that the greatest contribution to the integral occurs near 0. Approximate an integral using a specified method. In the context of NIntegrate usage, an integration rule object provides both an integral estimate and an error estimate as a measure of the integral. This answer is based on observations of the behavior of NIntegrate. The Monte Carlo methods in Mathematica are non-adaptive, so when you specify a certain MaxPoints, the integrand will be evaluated at all of these points, uniformly throughout the integration region, and this might be time consuming if the integrand does not converge easily. Numerically integrate functions that cannot be integrated symbolically. If you specify MaxPoints only but no method, then the QuasiMonteCarlo method is used. You can specify the number of points used in a MonteCarlo calculation by changing MaxPoints, otherwise a default value of 50000 will be used. Remember that in this type of method the error is proportional to 1/Sqrt, where N is the number of points used. One can also use the 'NIntegrate Explorer' to build knowledge or proficiency in determining NIntegrates methods by the plots of the sampling points. ![]() Trong Maple thì lnh sau > evalf (int (sqrt (1+ (x2-3)2),x1.5)) Cho ra kt qu: 31. Không bit Truong Chan ã nhp câu lnh th nào. ![]() ![]() In our experience the QuasiMonteCarlo method will give a more accurate answer than the MonteCarlo method. Có th nhp sai ch Mathematica là phn mm cc mnh, khó sai lm. But we are guaranteed to always get the same result. ![]()
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