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极坐标变换下二重积分解法探究

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二重积分计算难易关键是对积分区域、被积函数表达式做适当的变换,进而利于求解过程的简化.对含有x2+y2y的二重积分,将积分区域的曲线、被积函数分别作相应的标准化处理,然后借助极坐标变换做相应的求解,从中得知,标准化被积函数计算二重积分优于标准化积分区域计算二重积分.
On Solution of the Double Integral via Polar Coordinate Transformation
The key to the difficulty of double integration calculation is to make appropriate transforma-tions to the integration region and the expression of the integrand function,which facilitates the simplifica-tion of the solving process.For double integrals containing x2+y2,the curves and integrands in the inte-gration region are respectively standardized,and then solved using polar coordinate transformation.It is found that calculating double integrals using standardized integrands is better than calculating double inte-grals using standardized integration regions.

double integralpolar coordinate transformationintegral regionintegrand function

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菏泽学院数学与统计学院,山东菏泽 274000

二重积分 极坐标变换 积分区域 被积函数

2024

菏泽学院学报
菏泽学院

菏泽学院学报

影响因子:0.404
ISSN:1673-2103
年,卷(期):2024.46(5)