Mathematics
Undergraduate

この問題が分かりません。どなたか教えてくれませんか。

J₁₁-²²- 2²-y² dxdy, 1. T 2. 3. 4. D = {(x, y) | y ≥ 0} 5. T = -2-3-4-6 π

Answers

∬🇩 e⁻ˣ²⁻ʸ²dxdy
x=rcosθ,y=rsinθとおくと,|J|=rより
∫[0→∞]re⁻ʳ²dr・∫[0→π]dθ
=[-(1/2)e⁻ʳ²][0→∞]・π
=π/2

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