在球面坐标系下计算三重积分∫∫∫Ωz^2dv,Ω:x^2+y^2+z^2≤R^2,x^2+y^2+z^2≤2Rz.直角坐标系下答案为59兀R^5/480.
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![在球面坐标系下计算三重积分∫∫∫Ωz^2dv,Ω:x^2+y^2+z^2≤R^2,x^2+y^2+z^2≤2Rz.直角坐标系下答案为59兀R^5/480.](/uploads/image/z/12243702-30-2.jpg?t=%E5%9C%A8%E7%90%83%E9%9D%A2%E5%9D%90%E6%A0%87%E7%B3%BB%E4%B8%8B%E8%AE%A1%E7%AE%97%E4%B8%89%E9%87%8D%E7%A7%AF%E5%88%86%E2%88%AB%E2%88%AB%E2%88%AB%26%238486%3Bz%5E2dv%2C%26%238486%3B%EF%BC%9Ax%5E2%2By%5E2%2Bz%5E2%E2%89%A4R%5E2%2Cx%5E2%2By%5E2%2Bz%5E2%E2%89%A42Rz.%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BB%E4%B8%8B%E7%AD%94%E6%A1%88%E4%B8%BA59%E5%85%80R%5E5%2F480.)
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在球面坐标系下计算三重积分∫∫∫Ωz^2dv,Ω:x^2+y^2+z^2≤R^2,x^2+y^2+z^2≤2Rz.直角坐标系下答案为59兀R^5/480.
在球面坐标系下计算三重积分∫∫∫Ωz^2dv,Ω:x^2+y^2+z^2≤R^2,x^2+y^2+z^2≤2Rz.直角坐标系下答案为59兀R^5/480.
在球面坐标系下计算三重积分∫∫∫Ωz^2dv,Ω:x^2+y^2+z^2≤R^2,x^2+y^2+z^2≤2Rz.直角坐标系下答案为59兀R^5/480.