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I have simple question regarding double integrating a function.

J*Integrate[Integrate[Cos[ArcTan[Sqrt[(x - a)^2 + (y - b)^2]/L]], {b, -b, b}], {a, -a,a}]

The error message: "Unable to prove that integration limits {-a,a} are real. Adding
assumptions may help" appears.

I tried adding assumptions:

J*Integrate[Integrate[Cos[ArcTan[Sqrt[(x - a)^2 + (y - b)^2]/L]], {b, -b, b}, Assumptions -> {Re[x], Re[y], Re[a] > 0, Re[b] > 0}], {a, -a, a}, Assumptions -> {Re[x], Re[y], Re[a] > 0, Re[b] > 0}]

But this did not seem to help, the same error message appears. I tried a few different combination of assumptions but nothing seems to work.

Any help?

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    $\begingroup$ Re[x] calculates the real part of x; it does not indicate that $x$ is real. For that you should use Element[x, Reals]. See Element. $\endgroup$
    – MarcoB
    Commented Dec 7, 2022 at 0:09
  • $\begingroup$ I tried this, but still get the same error... $\endgroup$
    – M. Dogan
    Commented Dec 7, 2022 at 15:40

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