Hello! How do I double integrate over an implicit region, like an elipsis, using the wolframAlpha?
Hi Thiago,
I could suggest to use the free (!) tier of the Development Cloud instead:
It is more flexible and easier to make concise requests if you know a bit of the Wolfram Language. It looks like this:
So the code you would use is exactly the code in your related thread .
Cheers,
Marco
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}]
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