Feb 27, 2019 · I cannot find what is the integral of a cumulative distribution function $$\\int G(\\xi)d\\xi$$ I think it should be simple, but I have no idea where else to look for it.

Jan 20, 2021 · $\begingroup$ "Answers to the question of the integral of 1x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers" --- not completely correct: if they are both negative it also works. This is an improper integral and does not converge in the remaining cases. $\endgroup$ –

Feb 21, 2018 · I was trying to do this integral $$\int \sqrt{1+x^2}dx$$ I saw this question and its' use of hyperbolic functions. I did it with binomial differential method since the given integral is in a form of $\int x^m(a+bx^n)^p\,dx$ and I spent a lot of time on it so I would like to see if it can be done this way and where did I go wrong. $$\int(1+x^2 ...

For a definite integral with a variable upper limit of integration $\int_a^xf(t)\,dt$, you have ${d\over dx} \int_a^xf(t)\,dt=f(x)$. For an integral of the form $$\tag{1}\int_a^{g(x)} f(t)\,dt,$$ you would find the derivative using the chain rule. As stated above, the basic differentiation rule for integrals is:

For questions about the properties of integrals. Use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that describe the type of integral being considered. This tag often goes along with the (calculus) tag.

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(x)=C will have a slope of zero at point on the function.

The $\Sigma$ sign is a sigma and stands for "sum". In an integral you take the limit as $\delta x$ goes to zero. So we replace the sigma with another type of s: $\int$. And the $\delta$ gets changed to a d. So it is now written: $\int f(x) dx $ and it is the "integral of f(x) with respect to x". But the dx doesn't mean anything on it's own.

I am teaching Calc 1 right now and I want to give my students more interesting examples of integrals. By interesting, I mean ones that are challenging, not as straightforward (though not extremely

Mar 16, 2012 · The absolute value equals "the inside" when "the inside" is non-negative, and equals " (-) the inside" when "the inside is negative. So you need to find where "the inside" is zero (i.e. find the roots of $-2x^3 + 24x = 0$ and possibly split the integral into two or …

$\begingroup$ @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, move the dummy copy into the first integral to get a double integral.