高数二重积分。求详细解答 高数二重积分求大佬详细解答！！！详细！！！万分感谢
\u9ad8\u6570\u4e8c\u91cd\u79ef\u5206\uff0c\u6c42\u8be6\u7ec6\u89e3\u7b54
\u3010\u6ce8\uff1a\u2235∂P/∂y=∂Q/∂x, \u2234\u8be5\u66f2\u7ebf\u79ef\u5206\u4e0e\u8def\u5f84\u65e0\u5173\uff0c\u5176\u5728\u5355\u8fde\u901a\u57dfD\u4e0a\u6cbf\u95ed\u66f2\u7ebfL
\u7684\u79ef\u5206=0\u3011
16. \u79ef\u5206\u57df\u5bf9\u79f0\u4e8e x \u8f74\uff0c y \u7684\u5947\u51fd\u6570 2yx^3 \u79ef\u5206\u662f0.
I = \u222b\u222bx^2(x^2+y^2)dxdy \u5316\u6781\u5750\u6807
= \u222bdt\u222b r^2(cost)^2 r^2 rdr
= \u222b(cost)^2dt\u222b r^5dr
= \u222b(cost)^2dt[r^6/6]
= (32/3)\u222b(cost)^8dt = (64/3)\u222b(cost)^8dt
= (64/3)(7/8)(5/6)(3/4)(1/2)(\u03c0/2) = 35\u03c0/12
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