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本文首先介绍了变分与变积的相关理论知识。Firstly, the relevant theories of the variation and integrand are introduced.

同样，请记住，我们在问我们什么功能分化得到积。Again, remember that we're asking what function we differentiated to get the integrand.

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根据积分路径和被积函数的特点，讨论了相应的计算复积分的方法。It is based on the properties about the path of integration and the integrand function.

积分区域和被积函数结构是函数积分的两个关键点。The integral range and the integrand structure are the two key points of the function integral.

这种方法在计算劲度矩阵时，被积函数大为简化，因而具有实用意义。The method remarkably simplifies the integrand for the stiffness matrix, and therefore has practical significance.

针对这些问题都还记得，我们可以随时检查鉴别，并确保我们得到了积我们的答复。In all of these problems remember that we can always check our answer by differentiating and making sure that we get the integrand.

对称积分区域以及被积函数有与之相匹配的奇、偶性的积分，均可用对称性简便计算。The integration can be simplified calculated using symmetry if it has symmetric integral domain and its integrand has odd or even characteristic.

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在一元函数中，被积函数在闭区间上连续是牛顿-莱布尼兹公式成立的重要条件。To the unvaried function, the continuity of integrand function on closed interval is the important conditions which make Newton-Leibniz formula hold.

在一定条件下，对振荡积分值做贡献的主要来自被积函数在临界点附近的小区间的积分值。Under some conditions, the major contribution to the value of oscillatory integral comes from neighborhoods of those critical points of the integrand.

计算阻抗矩阵元素时，由于被积函数振荡性很强，收敛慢，难于计算。The integrand exhibits slowly convergence and highly oscillatory, which leads to difficulties when attempting to evaluate the impedance matrix elements.

在定积分计算中，当被积函数与上取整函数有关时，会有不同的表达形式。If the integrand is related to the top integral function in definite integral computation, the definite integral possesses the different expression from.

如果你还记得我们的所有要求是什么，我们得到的积区分这是很简单，但它有时似乎导致的问题。If you remember that all we're asking is what did we differentiate to get the integrand this is pretty simple, but it does seem to cause problems on occasion.

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积分区域的对称性和被积函数的奇偶性不仅体现了数学美，而且可以使积分的计算变得简单又方便。The symmetry of integral domain and the parity of integrand not only reflect the beauty of math, but also make integral computation more simple and convenient.

贝叶斯推断中边际似然函数涉及到维数较高的复杂积分的计算，因而精确地计算边际似然函数往往有困难。In Bayesian reference, marginal likelihood function involve to compute high dimensional complex integrand. So exactly to compute marginal likelihood is often difficult.

本文研究了涡流检测中放置式线圈阻抗积分的被积函数性态，解决了积分限的确定问题。In this paper, the integrand function of the impedance integral for air-cored probe coil is studied and the problem of the determination for the integral limits is resolved.

为了有限元列式的保辛，变分原理被积函数可导向对于对偶变量为对称的形式。In order to maintain the symplectic conservation conditions of FEM formulation, the integrand in the variational principle is rewritten in symmetrical form for duality variables.

在定积分和重积分的计算中，恰当地利用被积函数的奇偶性和积分区域的对称性，可以使积分运算大大简化。In the calculation of defining and double integral, appropriately making use of the odevity of integrand and the symmetry of integral region can simplify the calculation of integral.

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下面是第二步,在被积函数中，当然需要把,用u，v来替换，目标是把被积函数化为,只关于u和v的函数。The second thing to know is x y you need to of course substitute any x and y's in the integrand to convert them to u's and v's so that you have a valid integrand involving only u and v.

从不定积分的线性运算性质出发，给出了计算不定积分的被积函数线性组合化、降幂的积分原则，并结合实例分析了这一原则在不定积分计算中的指导作用。Based on the quality of linear operation about indefinite integral, the article puts forward an indefinite integral principle of making linear combination and reducing power of integrand.

积分式中的被积函数包含一噪声强度垂直指向性因子，海洋介质分层条件通过该指向性因子影响噪声场的空间相干。The integrand includes a multiplying factor of the vertical directivity of the noise intensity, and the layered ocean environment affects the spatial coherences via this directivity factor.