# [✓] Calculate a double Integrate over an ellipse region?

GROUPS:
 Hello! I have a simple question? How do I double integrate a function over an Elipsis Region? Something similar to a Circle Region, like Thanks in advance.
2 months ago
10 Replies
 Mariusz Iwaniuk 1 Vote Hello Integrate[1, {x, y} \[Element] Circle[{0, 0}, {a, b}]] but Mathematica 11.3 gives unevaluated answer:it should be: $4 a E\left(1-\frac{b^2}{a^2}\right)$You can use: ArcLength[Circle[{0, 0}, {a, b}]] (* 4 b EllipticE[1 - a^2/b^2] *) Regards,MI
2 months ago
 Works in my copy of 11.3 In[6]:= Assuming[a > 0 && b > 0, Integrate[1, {x, y} \[Element] Circle[{0, 0}, {a, b}]]] Out[6]= 2 (b EllipticE[1 - a^2/b^2] + a EllipticE[1 - b^2/a^2])
2 months ago
 Yes with Assumptions work in my copy to.Thanks.
2 months ago
 It also works without Assumptions, but returns (understandably) a much larger result and takes quite a bit of time. It might return unevaluated on a slower machine, I suppose.
2 months ago
 Indeed it does:Sorry for the late posting, but apparently every contribution to any thread only shows up much later for me than for many others on the Community. Cheers,Marco
2 months ago
 Well, these might work, too: Integrate[1, {x, y} \[Element] RegionBoundary[Ellipsoid[{0, 0}, {r1, r2}]], Assumptions -> {r1 > 0, r2 > 0}] This gives the same answer (on 11.3) Integrate[1, {x, y} \[Element] Circle[{0, 0}, {r1, r2}], Assumptions -> {r1 > 0, r2 > 0}] Cheers,Marco
2 months ago
 Thanks for the response! But, I have another doubt, I was expecting a number as a result (like a volume). What Do I Have to do with EllipticE?