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Integrals are the powerful tools that provide deep insights into the behavior of functions and are essential for modelling and understanding the world of human being. Integration has widespread applications across various fields. Integrals are used to calculate accumulation processes and find the area under curves. This is crucial in physics by calculating displacement from velocity and in various engineering and economic applications by calculating total profit from a production function. Integrals are used in probability theory and statistics for calculating probabilities and expected values. In statistical applications, integration plays a significant role in calculating areas under probability distributions, which are used in hypothesis testing and confidence intervals. Solving a complex integral is too tough if just use some fundamental formulas. The techniques of integration include substitutions, integral by parts, integration using Trigonometric Identities, fixed formulas of integration. This essay is going to introduce some of the most important methods of integration.
Jikang Xiang (Fri,) studied this question.