Dec 15, 2017 · A different type of integral, if you want to call it an integral, is a "path integral". These are actually defined by a "normal" integral (such as a Riemann integral), but path …

Jan 20, 2021 · 16 Answers to the question of the integral of 1 x 1 x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers. If we …

@user599310, I am going to attempt some pseudo math to show it: $$ I^2 = \int e^-x^2 dx \times \int e^-x^2 dx = Area \times Area = Area^2$$ We can replace one x, with a dummy variable, …

Nov 29, 2013 · Wolfram Mathworld says that an indefinite integral is "also called an antiderivative". This MIT page says, "The more common name for the antiderivative is the …

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 …

Aug 9, 2017 · the short answer is that the integral of the derivative is the original function, up to a constant. Of course, (1) isn't true without restrictions. But if f ′ is continuous, then, yes, (1) holds.

One possible interpretation: a "normal" integral is simply a line integral where the path is straight and oriented along a particular axis. Thus, as soon as you perform a transformation to the …

Feb 17, 2025 · So an improper integral is a limit which is a number. Does it make sense to talk about a number being convergent/divergent? It's fixed and does not change with respect to the …

Mar 16, 2012 · To expand on @davin's comment: Use the definition of the absolute value! The absolute value equals "the inside" when "the inside" is non-negative, and equals " (-) the …

In calculus we've been introduced first with indefinite integral, then with the definite one. Then we've been introduced with the concept of double (definite) integral and multiple (definite) integ...