Double Integrals: Evaluate I for Domain D

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to evaluate the integral:

I=dxdy/(x^2+y^2)^(1/2)


over domain D:
given by 1<=x^2+y^2<=4.

what should i take the limits to integral?
dx and dy
 
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Hi splelvis! Welcome to PF! :smile:

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splelvis said:
… over domain D:
given by 1<=x^2+y^2<=4.

what should i take the limits to integral?
dx and dy

One of the limits will be -2 to 2 … let's say for y.

Then just look at the graph …

for a fixed value of y, what does x go from and to? :smile:
 
thank you i got that
 
Hello,
I think polar coordinates is a good choice for this one. :)
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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