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Calculate a double integrate over an implicit region using W|A?

Posted 6 months ago
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Hello! How do I double integrate over an implicit region, like an elipsis, using the wolframAlpha?

3 Replies

Hi Thiago,

I could suggest to use the free (!) tier of the Development Cloud instead:

https://www.wolframcloud.com

It is more flexible and easier to make concise requests if you know a bit of the Wolfram Language. It looks like this:

enter image description here

So the code you would use is exactly the code in your related thread.

Cheers,

Marco

Posted 6 months ago

Thanks, Marco. But, I'm looking for the "Step-by-Step" solution thats is built-in on Wolfram, thats the reason I mentioned it

Hi, I do not think that you will get an automatic step-by-step solution for this. But this looks like a textbook example, which is easy to solve. You still integrate over a disk - a shifted unit disk:

ContourPlot[x^2 + y^2 - 2 y == 0, {x, -2, 3}, {y, -2, 3}]

enter image description here

So if you introduce the new variable z->y-1, you obtain a unit disk:

Simplify[x^2 + y^2 - 2 y == 0 /. y -> z + 1]
(*x^2 + z^2 == 1*)

So the new integral is

Integrate[1, {x, z} \[Element] Disk[]]

In polar coordinates this is:

Integrate[r, {\[Phi], 0, 2 Pi}, {r, 0, 1}]

which evaluates to Pi. So even if Mathematica doesn't show you the step-by-step solution it is really easy to perform a step by step calculation.

Cheers, Marco

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