Based on some known results and simple technique, we emphasize in this article, certain nonlinear dynamic integral inequalities in one variable on timescales. Part of the novelty herein not only unifies and extends some integral inequalities related to different cases of positive constants but also explores the explicit bounds for discontinuous functions on timescales. We contribute to the ongoing research by providing mathematical results that can be used as necessary tools in the theory of certain classes of differential, integral, finite difference and sum–difference equations on timescales. The consequences of the computational experiments show that the proposed strategy can produce adequate and reliable results. Examples are also discussed to demonstrate the importance of the tests.

中文翻译：

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动态积分不等式的计算方法及其在时间尺度微积分中的应用

基于一些已知的结果和简单的技术，我们在本文中强调在一个时标上某个变量的某些非线性动态积分不等式。本文的部分新颖性不仅统一和扩展了与正常数的不同情况有关的一些积分不等式，而且还探索了时间尺度上不连续函数的显式界。我们通过提供数学结果作为时态上某些类型的微分，积分，有限差分和和差分方程的理论的必要工具，为正在进行的研究做出了贡献。计算实验的结果表明，所提出的策略可以产生足够而可靠的结果。还讨论了一些示例以证明测试的重要性。