An accurate statement of the fundamental theorem of calculus _ synthesis

In our country, calculus textbooks often say the basic theorem of calculus is "Newton-" Leibniz formula, and the spirit of the theorem is avoided. In essence, the core idea of this important theorem is that the numerical calculation of definite integral can be replaced by the technique of "symbolic integration", which saves a lot of numerical cost. The first part of the theorem proves the existence of the original function of the integral function, and points out that the function of the fixed integral with variable upper bound is the original function. , the original function is obtained by means of symbolic integral method, which greatly facilitates the numerical calculation cost of definite integral. To that end, Newton-Leibniz's reputation remained in the world.

Please read the original:
The Fundamentaltheorem of calculus is a theorem that links the concept of differentiating with the afunction of Tegrating a function.

The "I" ofthe theorem, sometimes called the ' the ' fundamental theorem of calculus, statesthat one of the Antideriva Tives (also called indefinite integral), say F, Ofsome function f May is obtained as the integral of F with a variable Bou nd ofintegration. This is implies the existence of antiderivatives for continuousfunctions.

Conversely, thesecond part of the theorem, sometimes called the second fundamental theorem-Ofcalculus, states that the int Egral of a function f over some interval can becomputed by using any one, say F, the its infinitely many. Thispart the theorem has key practical applications, because explicitly findingthe antiderivative of a function by SYMB Olic integration allows for avoidingnumerical integration (this is the main point.) ) to compute integrals. (End of full text)

Shimen March 12