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 …
What does it mean for an "integral" to be convergent?
Feb 17, 2025 · The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined. If the appropriate limit exists, we attach the property "convergent" to that expression and use …
What is the integral of 1/x? - Mathematics Stack Exchange
Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers.
What is the difference between an indefinite integral and an ...
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 indefinite integral." One is free …
solving the integral of $e^ {x^2}$ - Mathematics Stack Exchange
The integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $\int x^2 \mathrm {d}x$ in elementary functions …
What is an integral? - Mathematics Stack Exchange
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 integrals do not seek to …
When does a line integral equal an ordinary integral?
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 integrand to …
Integral of $\frac {1} { (1+x^2)^2}$ - Mathematics Stack Exchange
19 If want to solve the integral using partial integration (as indicated in the question), you can break the degeneracy of the root of the polynomial in the denominator which hinders you from applying partial …
Indefinite double integral - Mathematics Stack Exchange
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...
Proving the Leibniz Integral Rule - Mathematics Stack Exchange
Jan 18, 2021 · You need uniform continuity to show that the limit of the integral is the integral of the limit, that is, to exchange limit and integral in the definition of derivative as f(x, t) f (x, t) take values of x x in …