1, Newton-Leibniz formula is a bridge between differential calculus and integral calculus, and it is one of the most basic formulas in calculus. It is proved that differential and integral are reversible operations, and it marks that calculus has formed a complete system in theory, and calculus has since become a real discipline.

2. Newton-Leibniz formula is the pillar of integral theory. Newton-Leibniz formula can be used to prove the definite integral substitution formula, the first mean value theorem of integral and Taylor formula of integral remainder. Newton-Leibniz formula can also be extended to double integral and curve integral, from one dimension to multiple dimensions.

The use of Newton-Leibniz formula;

1 and Newton-Leibniz formulas are also widely used in physics, calculating the distance of moving objects, calculating the work done by variable force along a straight line and the universal gravitation between objects.

2. Newton-Leibniz formula promotes the development of other branches of mathematics, which are embodied in differential equations, Fourier transform, probability theory, complex variable functions and other branches of mathematics.

Extended data:

The contents of 1 and Newton-Leibniz formulas are that the definite integral of a continuous function in the interval [a, b] is equal to the increment of any of its original functions in the interval [a, b]. Newton described this formula with kinematics in the Introduction to Flow Number written by 1666, and Leibniz formally proposed this formula in a manuscript written by 1677. Because they first discovered this formula, they named it Newton-Leibniz formula.

2. Newton-Leibniz formula shows that the definite integral of the function can be calculated by any anti-missile function of the function. This part is a key and widely used theorem in calculus or mathematical analysis, because it greatly simplifies the calculation of definite integral.