What is Newton Leibniz Theorem?
Answers
Hello buddy here is your answer
Newton-Leibniz formula
2010 Mathematics Subject Classification: Primary: 26A06 Secondary: 26A46 [MSN][ZBL]
The formula expressing the value of a definite integral of a given integrable function f over an interval as the difference of the values at the endpoints of the interval of any primitive (cf. Integral calculus) F of the function f:
∫abf(x)dx=F(b)−F(a).(1)
It is named after I. Newton and G. Leibniz, who both knew the rule expressed by 1, although it was published later. It is also known as "Fundamental theorem of calculus".
If f is Lebesgue integrable over [a,b] and F is defined by
F(x)=∫axf(t)dt+C,
where C is a constant, then F is absolutely continuous, F′(x)=f(x) almost-everywhere on [a,b] (everywhere if f is continuous on [a,b]) and 1 is valid.
A generalization of the Newton–Leibniz formula is the Stokes formula for orientable manifolds with a boundary.
References
[Ru] W. Rudin, "Real and complex analysis" , McGraw-Hill (1966).
[St] K.R. Stromberg, "Introduction to classical real analysis" , Wadsworth (1981).
I hope my answer will help you
Please mark my answer as Brainlist
Answer:
Newton-Leibniz formula. ... It is also known as "Fundamental theorem of calculus". If f is Lebesgue integrable over [a,b] and F is defined by F(x)=x∫af(t)dt+C, where C is a constant, then F is absolutely continuous, F′(x)=f(x) almost-everywhere on [a,b] (everywhere if f is continuous on [a,b]) and 1 is valid.