Chapter 5, definite integral
Knowledge logic structure diagram
Postgraduate exam content
The concept of definite integral (application of the limit) and basic properties (pay attention to the position of the upper and lower limits, linearity, between partitions, and the estimation theorem of the ratio when the upper limit is greater than the lower limit), the median value theorem of definite integrals, express and calculate the centroid with definite integrals, The function of the upper limit of the integral and its derivative, the Newton-Leibniz formula, the method of definite integral replacement (change the yuan thoroughly, don’t forget that the upper and lower limits of the dx definite integral must be changed as well) and Integration by parts, integration of rational functions, rational expressions of trigonometric functions and simple irrational functions, generalized integration concepts and calculations.
Postgraduate exam requirements
- 1. Able to find the integrals of rational functions, trigonometric functions, and simple irrational functions.
- 2. Understand the function of the upper limit of the integral, and find its derivative (far more useful than this, often combined with Rolle's theorem to solve the zero point problem), and master the Newton-Leibniz formula.
- 3. Understand the concept of generalized integral, and can calculate generalized integral (using the point of view of limit).
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