mathematica计算重积分时出了问题(结果是零和预期的结果不一样)求解错误.截图可能看的不清楚代码是这样的Integrate[(z - a)/(Sqrt[(x^2 + y^2 + (z - a)^2)]^3),{z,- R,R},{y,- Sqrt[R^2 - z^2],Sqrt[R^2 - z^2]},{x,- S
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![mathematica计算重积分时出了问题(结果是零和预期的结果不一样)求解错误.截图可能看的不清楚代码是这样的Integrate[(z - a)/(Sqrt[(x^2 + y^2 + (z - a)^2)]^3),{z,- R,R},{y,- Sqrt[R^2 - z^2],Sqrt[R^2 - z^2]},{x,- S](/uploads/image/z/8628086-38-6.jpg?t=mathematica%E8%AE%A1%E7%AE%97%E9%87%8D%E7%A7%AF%E5%88%86%E6%97%B6%E5%87%BA%E4%BA%86%E9%97%AE%E9%A2%98%EF%BC%88%E7%BB%93%E6%9E%9C%E6%98%AF%E9%9B%B6%E5%92%8C%E9%A2%84%E6%9C%9F%E7%9A%84%E7%BB%93%E6%9E%9C%E4%B8%8D%E4%B8%80%E6%A0%B7%EF%BC%89%E6%B1%82%E8%A7%A3%E9%94%99%E8%AF%AF.%E6%88%AA%E5%9B%BE%E5%8F%AF%E8%83%BD%E7%9C%8B%E7%9A%84%E4%B8%8D%E6%B8%85%E6%A5%9A%E4%BB%A3%E7%A0%81%E6%98%AF%E8%BF%99%E6%A0%B7%E7%9A%84Integrate%5B%28z+-+a%29%2F%28Sqrt%5B%28x%5E2+%2B+y%5E2+%2B+%28z+-+a%29%5E2%29%5D%5E3%29%2C%7Bz%2C-+R%2CR%7D%2C%7By%2C-+Sqrt%5BR%5E2+-+z%5E2%5D%2CSqrt%5BR%5E2+-+z%5E2%5D%7D%2C%7Bx%2C-+S)
mathematica计算重积分时出了问题(结果是零和预期的结果不一样)求解错误.截图可能看的不清楚代码是这样的Integrate[(z - a)/(Sqrt[(x^2 + y^2 + (z - a)^2)]^3),{z,- R,R},{y,- Sqrt[R^2 - z^2],Sqrt[R^2 - z^2]},{x,- S
mathematica计算重积分时出了问题(结果是零和预期的结果不一样)求解错误.
截图可能看的不清楚
代码是这样的
Integrate[(z - a)/(Sqrt[(x^2 + y^2 + (z - a)^2)]^3),{z,- R,
R},{y,- Sqrt[R^2 - z^2],
Sqrt[R^2 - z^2]},{x,- Sqrt[R^2 - z^2 - y^2],
Sqrt[R^2 - z^2 - y^2]},Assumptions -> {R > 0,a > 0,R > a}]
mathematica计算重积分时出了问题(结果是零和预期的结果不一样)求解错误.截图可能看的不清楚代码是这样的Integrate[(z - a)/(Sqrt[(x^2 + y^2 + (z - a)^2)]^3),{z,- R,R},{y,- Sqrt[R^2 - z^2],Sqrt[R^2 - z^2]},{x,- S
需要输入R的具体数值
如
In[3]:= R = 1;
Integrate[(z - a)/(Sqrt[(x^2 + y^2 + (z - a)^2)]^3),{z,-R,
R},{y,-Sqrt[R^2 - z^2],
Sqrt[R^2 - z^2]},{x,-Sqrt[R^2 - z^2 - y^2],
Sqrt[R^2 - z^2 - y^2]},Assumptions -> {R > 0,a > 0,R > a}]
Out[4]= -((4 a \[Pi])/3)