关键词: Monte-Carlo方法, 平均值法, 频数法

Abstract: In view of the solution of the definite integral approximate calculation question, the paper gives an algorithm to calculate definite integral based on the Monte-Carlo method, which is abbreviated to mean value law and different from the frequency law which is used by the people in usual. The theory basis of this algorithm is the mathematic expectation theorem and the law of large numbers in theory of probability. First, a group of random numbers can be gained by throwing spots randomly to the integrating range. Second, the function value corresponded by each random number composes a group of random variables. At last, the definite integral approximate value is gained by the random variable mean value multiplying the length value of the integrating range. Because of the randomness of this algorithm, it can be fully calculated using the network at the same time. The experimental result indicates this algorithm is effective. Compared with the frequency law, it is of better accuracy and time efficiency.

Key words: Monte-Carlo method, mean value law, frequency law