calculus - Why is the area under a curve the integral? - Mathematics ...
Dec 23, 2010 · One is the question of why the definite Riemann integral gives the correct notion of "area under a curve" for a (nonnegative, Riemann integrable) function. The other, which seems to be what …
Difference between indefinite and definite integration: $\int f (x ...
Sep 13, 2019 · Fundamental Theorem of Calculus The definite and the indefinite integral are linked by the Fundamental Theorem of Calculus as follows: In order to compute a definite integral, find the …
real analysis - What is the difference between Definite Integral ...
Jun 7, 2016 · The definite integral is by definition a limit of a certain class of sums (the class of the Riemann sums, by the way): no relation a priori with the derivatives. The indefinite integral is by …
Difference Between Riemann Integrals and Definite Integrals
Jul 2, 2023 · The Riemann integral follows various "intuitive" notions of area, for example if you split an interval up then the integral over the whole interval is equal to the sum of its parts, if you add two …
What does infinity as an upper/lower limit mean in a definite integral ...
Dec 4, 2020 · 2 I was finding $$\int_0^\infty e^ {-x} dx$$ So the integral becomes $$\left. (-e)^ {-x}\right\rvert_0^\infty$$ Now here's the confusing thing for me. What exactly does infinity mean in …
Difference between integral, anti-derivative, and definite integral?
Dec 2, 2016 · Bottom line: antiderivative --- one function indefinite integral --- set of functions definite integral --- number. As mentioned in a comment, antiderivatives and definite integrals are related by …
What is the integral of 0? - Mathematics Stack Exchange
Feb 4, 2018 · The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that the derivative of the function is the function's slope, because any function f …
The negative integral meaning - Mathematics Stack Exchange
Jul 19, 2014 · Whenever I take a definite integral in aim to calculate the area bound between two functions, what is the meaning of a negative result? Does it simly mean that the said area is under …
Why do we not include $c$ in the computation of the definite integral?
Apr 2, 2016 · The definite integral is different in the sense that it evaluates either to a number (in the single variable case) or a function independent of the variable of integration (in the multivariable case).
Definite Integral and Constant of Integration
Jun 10, 2012 · A definite integral is nothing different from an indefinite integral but the constant, that was eliminated during the differentiation, has some definite value. For instance in indefinite integrals we …