求二重积分,被积函数是e……(y/x+y),积分区域是x+y=2,x轴,y轴围成的三角形内.写错了……被积函数是e^(y/x+y)
问题描述:
求二重积分,被积函数是e……(y/x+y),积分区域是x+y=2,x轴,y轴围成的三角形内.
写错了……被积函数是e^(y/x+y)
答
选用极坐标系,积分区域 D:0≤ θ ≤ π/2,0 ≤ r ≤ 2/(sinθ+cosθ) I = ∫[0,π/2] dθ ∫[0,2/(sinθ+cosθ)] e^[sinθ/(sinθ+cosθ)] * r dr= ∫[0,π/2] e^[sinθ/(sinθ+cosθ)] * 2/(sinθ+cosθ)² dθ...