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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

1 vote
1 answer
154 views

How to prove this integral equality with limits

The following result is from a paper. The author says it is not hard to show that: $$\lim_{t\to 1}\dfrac{1-t}{\sqrt{1+pt}}\int_{0}^{t}\dfrac{a(1+pa)}{(1-a)^2}\left(4a\left[1-\left(\dfrac{1-t}{1-a} …
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24 votes
2 answers
1k views

Is $\iiint_{[0, 1]^3} \lvert f(x)+f(y)+f(z)\rvert\, dx\, dy\, dz \ge \int_0^1 \lvert f(x)\rv...

$\newcommand\abs[1]{\lvert#1\rvert}\newcommand\Abs[1]{\left\lvert#1\right\rvert}$Question: Let $f(x)$ be a continuous real-valued function defined on the interval $[0, 1]$. Does the following inequalit …
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2 votes
0 answers
246 views

A integral equation with Discrete to result by inverse problem

Problem I asked a question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here, (I know the questi …
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