Some Physically Useful Definite Integrals一些物理上有用的定积分
This is just a sampling of some of the definite integrals which appear in physical problems 这仅仅是物理问题中出现的一些定积分的示例
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Definite Integrals Associated with Gaussian Distributions与高斯分布相关的定积分
In physical systems which can be modeled by a Gaussian distribution, one sometimes needs to obtain the average or expectation value for physical quantities. If these properties depend on x, then they can be integrated to find the average value. For the first five powers of x, the integrals have the following forms: 在可以由高斯分布建模的物理系统中，有时需要计算物理量的平均值或期望值。如果这些性质依赖于x，则可以通过积分来求得平均值。对于x的前五个幂次，积分形式如下：
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Definite Integrals of the Squares of Trig Functions三角函数平方的定积分
In dealing with sinusoidal functions associated with waves and those associated with AC electric circuits, the squares of trig functions appear. If they are averaged, then the average of the square of a trig function is found to be 1/2, so long as you are taking an integer number of quarter periods. 在处理与波相关的正弦函数以及与交流电电路相关的正弦函数时，三角函数的平方会出现。如果对它们进行平均，那么三角函数平方的平均值被发现为1/2，只要你取的是整数个四分之一周期。
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