计算二重积分I=∫∫ x/(x²+y²)dxdy,其中D为区域x²+y²≤1,x≥0,y≥0.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 19:34:54
![计算二重积分I=∫∫ x/(x²+y²)dxdy,其中D为区域x²+y²≤1,x≥0,y≥0.](/uploads/image/z/2409849-9-9.jpg?t=%E8%AE%A1%E7%AE%97%E4%BA%8C%E9%87%8D%E7%A7%AF%E5%88%86I%3D%E2%88%AB%E2%88%AB+x%2F%28x%26%23178%3B%2By%26%23178%3B%29dxdy%2C%E5%85%B6%E4%B8%ADD%E4%B8%BA%E5%8C%BA%E5%9F%9Fx%26%23178%3B%2By%26%23178%3B%E2%89%A41%2Cx%E2%89%A50%2Cy%E2%89%A50.)
x){nuӟy|m:VBFv%LHyںɎ.Ovzڳhu.1ԩxԹ@D$;i{AF$5/h-J)Rx6 ?ٽY"M^.b֔"htqf}#M] VP <;/
计算二重积分I=∫∫ x/(x²+y²)dxdy,其中D为区域x²+y²≤1,x≥0,y≥0.
计算二重积分I=∫∫ x/(x²+y²)dxdy,其中D为区域x²+y²≤1,x≥0,y≥0.
计算二重积分I=∫∫ x/(x²+y²)dxdy,其中D为区域x²+y²≤1,x≥0,y≥0.
原式=∫dθ∫[(rcosθ)/r²]rdr (极坐标代换)
=∫cosθdθ∫dr
=[sin(π/2)-sin0](1-0)
=1.