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I want to calculate surface area like this

Integrate[Boole[x^2 + y^2 < 1], {x, -1, 1}, {y, -1, 1}]

But Wolafram Mathematica said: invalid integration variable or limit(s) in {39/5, -1, 1}

What's the problem?

I looked at the official documentation but their examples give the same error. Moreover, it only works when adding a second integration variable.

GumBlor
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  • What version are you running? Under `13.2.0 for Linux x86 (64-bit) (December 12, 2022)` this `Integrate[Boole[x^2+y^2<1],{x,-1,1},{y,-1,1}]` returns `π` Perhaps try `Integrate[Integrate[Boole[x^2+y^2<1],{x,-1,1}],{y,-1,1}]` which some VERY old advice made some examples work. I don't understand exactly what you mean by your last sentence, can you explain that more precisely? Or search through all the answers here: `https://mathematica.stackexchange.com/search?q=integrate+boole` for other ideas which helped other people in the past. – Bill Jun 11 '23 at 14:01

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