定积分换元法是定积分计算的主要方法之一。
The method of the definite integral by substitution is one of the main techniques among the definite integral calculation.
本文给出了计算三角复合函数的定积分的若干方法。
In this paper we obtain several theorem of the definite integral of triangle composite function.
但几种特殊类型的定积分的计算却是难点。
However, some kinds of special type of definite integrals are difficult to calculate.
本文推广和改进了定积分近似计算的矩形公式。
In this paper, we extend and improve the rectangle formula of definite integrals 'approximate calculation.
该定积分可用MATLAB提供的积分函数计算，或者利用蒙特卡罗方法通过编程求解。
The definite integral can be calculated with the integration function in MATLAB or can be solved by using the Monte Carlo programming method.
对于定积分近似计算中常使用的经典SIMPSON求积公式介绍一种新的简洁的证明方法并给出误差的最佳估计。
We introduced a new and simple proof of the classical SIMPSON quadrature formula which is frequently applied in calculating definite integrals and best estimation of error is obtained.
告诫学生使用高斯公式计算曲面积分时一定不能忽视条件，否则可能导致错误。
It reminds the learners to notice the formula premise when using Gauss Formula, to avoid obtain a wrong result.
对称区间上的定积分和一类非对称区间上的定积分，均可用对称原理简便计算。
The paper discusses the use of symmetry principle in the evaluating of definite integrals on both the symmetric interval and non-symmetric interval.
定积分的计算是高等数学的重要内容之一，但在积分计算时可以结合积分区域的对称性和被积函数的奇偶性来简化计算。
Optimal calculation of definite integral can be obtained by combination of the odevity of function and the symmetry of integral domain.
数值积分算例表明，该算法得到的积分值精度高，自适应强，是一种有效的数值积分方法，在数值计算和工程实际应用中具有一定的参考和应用价值。
Simulation examples of integral show the algorithm is a validated method with high precision and powerful self-adapting. The algorithm has value in numerical calculation and engineering practice.
数值计算结果证明，该算法可以快速计算通常意义下任意函数的定积分，并能计算振荡函数的积分。
Numerical experimental results prove that the algorithm can compute integral for any functions in the usual sense, and compute oscillation function integral.
数值计算结果证明，该算法可以快速计算通常意义下任意函数的定积分，并能计算振荡函数的积分。
Numerical experimental results prove that the algorithm can compute integral for any functions in the usual sense, and compute oscillation function integral.
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