∫∫(D)arctan y/x dxdy. D:1≤x^2+y^2≤4,y≥0,y≤xx=rcosθ y=rsinθ ∫∫(D)arctan y/x dxdy=∫∫(D')arctan(sinθ/cosθ)rdrdθ 其中D':1π/4)∫(1->2)θr dr dθ是怎么化简的
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![∫∫(D)arctan y/x dxdy. D:1≤x^2+y^2≤4,y≥0,y≤xx=rcosθ y=rsinθ ∫∫(D)arctan y/x dxdy=∫∫(D')arctan(sinθ/cosθ)rdrdθ 其中D':1π/4)∫(1->2)θr dr dθ是怎么化简的](/uploads/image/z/11160524-20-4.jpg?t=%E2%88%AB%E2%88%AB%28D%29arctan+y%2Fx+dxdy.+D%3A1%E2%89%A4x%5E2%2By%5E2%E2%89%A44%2Cy%E2%89%A50%2Cy%E2%89%A4xx%3Drcos%CE%B8+y%3Drsin%CE%B8+%E2%88%AB%E2%88%AB%28D%29arctan+y%2Fx+dxdy%3D%E2%88%AB%E2%88%AB%28D%27%29arctan%28sin%CE%B8%2Fcos%CE%B8%29rdrd%CE%B8+%E5%85%B6%E4%B8%ADD%27%3A1%CF%80%2F4%29%E2%88%AB%281-%3E2%29%CE%B8r+dr+d%CE%B8%E6%98%AF%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E7%9A%84)
∫∫(D)arctan y/x dxdy. D:1≤x^2+y^2≤4,y≥0,y≤xx=rcosθ y=rsinθ ∫∫(D)arctan y/x dxdy=∫∫(D')arctan(sinθ/cosθ)rdrdθ 其中D':1π/4)∫(1->2)θr dr dθ是怎么化简的
∫∫(D)arctan y/x dxdy. D:1≤x^2+y^2≤4,y≥0,y≤x
x=rcosθ y=rsinθ ∫∫(D)arctan y/x dxdy=∫∫(D')arctan(sinθ/cosθ)rdrdθ 其中D':1<=r<=2,0<=θ<=π/4 那么 ∫∫(D)arctan y/x dxdy=∫∫(D')arctan(sinθ/cosθ)rdrdθ= ∫(0->π/4)∫(1->2)θr dr dθ= ∫(0->π/4) θ/2*r^2|(1->2) dθ= ∫(0->π/4) θ/2*(4-1) dθ= 3/4*θ^2|(0->π/4)=3π^2/64 其中∫∫(D')arctan(sinθ/cosθ)rdrdθ= ∫(0->π/4)∫(1->2)θr dr dθ是怎么化简的
∫∫(D)arctan y/x dxdy. D:1≤x^2+y^2≤4,y≥0,y≤xx=rcosθ y=rsinθ ∫∫(D)arctan y/x dxdy=∫∫(D')arctan(sinθ/cosθ)rdrdθ 其中D':1π/4)∫(1->2)θr dr dθ是怎么化简的
∫∫(D')arctan (sinθ/cosθ)rdrdθ= ∫∫(D')arctan(tan θ)rdrdθ = ∫∫(D') θrdrdθ