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 …

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 …

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...

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 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 · So, I can intuitively grasp that the derivative of the integral of a given function brings you back to that function. Is this also the case with the integral of the derivative?

Apr 26, 2019 · In your case, your first integral is your solution. Actually for first order differential equation integral and solution are equivalent. Let's come to the answer of your second query …

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 …

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 ...

May 28, 2021 · I am having difficulties to compute this integral $$ \int_ {-\infty}^\infty e^ {\pm ix^2} \, dx. $$ I tried to use complex integration and Cauchy's theorem but it didn't work. Can …