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 …

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 …

What is the integral of $$\int_ {-\infty}^ {\infty}e^ {-x^2/2}dx\,?$$ My working is here: = $-e^ (-1/2x^2)/x$ from negative infinity to infinity. What is the value of this?

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 …

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 …

Jan 5, 2026 · I need help with the following integral. $$ \mathrm {P}\!\int_ {-\infty}^ {\infty} \frac {\cos x} {x+a}\,dx, \qquad 0<a<1. $$ P is Cauchy's Principal Value. The first ...

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.

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...

Definite integrals of that function are found by numerical methods rather than by finding a closed-form antiderivative. In exercises of this kind usually one gets the value of the integral either …