Questions tagged [bounds-of-integration]
In many questions the problem of determining bounds of integration in multiple integrals is a major part of what an answer needs to deal with, and in surprisingly many questions it is the only issue. This tag is for such occasions.
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Integrating the bivariate normal distribution [duplicate]
Let $X$ and $Y$ have the bivariate normal density function,
$$ f(x, y) = \frac{1}{2 \pi \sqrt{1 - p^2}} \exp \left\{ - \frac{1}{2(1 - p^2)} (x^2 - 2pxy + y^2) \right\} $$
for fixed $p \in (-1, 1)$. ...
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Double Integral $\int\limits_0^1\!\!\int\limits_0^1\frac{(xy)^s}{\sqrt{-\log(xy)}}\,dx\,dy$
Is it possible to get a closed form of the following integral?
$$I=\int_0^1\!\!\!\int_0^1\frac{(xy)^s}{\sqrt{-\log(xy)}}\,dx\,dy\quad\quad\quad(s>0).$$
My attempt: I’ve tried a change of variables ...
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Change of variables Double integral
I have
$$\iint_A \frac{1}{(x^2+y^2)^2}\,dx\,dy.$$
$A$ is bounded by the conditions $x^2 + y^2 \leq 1$ and $x+y \geq 1$.
I initially thought to make the switch the polar coordinates, but the line $x+...
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