定积分在概率论中的应用教学案例研究

——以连续型随机变量为例

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中图分类号：G642 文献标识码：A DOI：10.16400/j.cnki.kjdk.2025.28.014

A Case Study on the Application ofDefinite Integrals in Probability Theory Teaching

-TakingContinuousRandomVariablesasanExample

XU Yongxin

（JinzhongNormal Junior College，Jinzhong，Shanxi O30600）

AbstractIntheteachingofprobabilitytheory，definiteintegrals，asacoremathematicaltool，arecloselyrelatedto thetheoryofcontinuous randomvariables.Given the teachingdificulties causedbytheabstractnatureofprobability calculations forcontinuous randomvariables，this paperfocusesontheapplicationofdefinite integrals inteaching.It elaborateson theintrinsic connection betweendefinite integralsand continuous random variables，designs typical teachingcases，andproposesanoptimized teaching strategybasedoncognitiveconstructionandcapabilityprogression. It aims to provideanoperable practicalpath and theoretical reference forthe teachingofprobability theory，which is of great significance for deepening the application of mathematical tools in probability teaching.

概率论作为数学学科的重要分支，在自然科学、工程技术及社会科学等领域应用广泛。（剩余4266字）