10/02/27 17:22:51
>>481
x=r*cosθ，y=r*sinθ とおくと積分範囲は
0<r<2cosθ、 -π/2<θ<π/2
だとおもいます
∬_[D] √(x^2+y^2) dxdy
= ∫_[-π/2, π/2] {∫_[0, 2cosθ] r^2 dr} dθ
= (8/3)∫_[-π/2, π/2] (cosθ)^3 dθ
= 32/9
URLﾘﾝｸ(www59.wolframalpha.com)
で
integrate integrate r^2 dr from r=0 to 2cos t dt from t=-pi/2 to pi/2
を入力すると楽です