Newton's formula, also known as the basic theorem of calculus, reveals the relationship between definite integral and the original function or indefinite integral of the integrand function. Newton-Leibniz formula, also known as the basic theorem of calculus, states that if the function f(x) is continuous in the closed interval [a, b] and the original function F (x) exists, then f(x) can be integrated on [a, b], and the definite integral from a to b (the lower limit of the integral number is a and the upper limit is b): ff (.

The meaning of Newton's formula:

The discovery of Newton-Leibniz formula makes people find a general method to understand the length of the formula curve, the area surrounded by the curve and the volume surrounded by the surface. The calculation of definite integral is simplified. As long as we know the original function of the integrand, we can always find the exact value of the definite integral or the approximate value of the first definite precision. 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. 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.