求曲线r=1,r=2cosθ所围成的公共部分的面积 大一高数定积分求面积 求由两曲线r=3cosθ与r=1+co...

\u5b9a\u79ef\u5206\u6c42\u66f2\u7ebfr=1,r=2cos\u03b8\u6240\u56f4\u516c\u5171\u90e8\u5206\u7684\u9762\u79ef

\u5b9a\u79ef\u5206\u6c42\u9762\u79ef\u7684\u9898\u76ee\u6c42\u6781\u5750\u6807\u65b9\u7a0b\u8868\u793a\u7684\u66f2\u7ebfr=a(1+cos\u03b8)\u4e0er=a\u6240\u56f4\u6210\u7684\u516c\u5171\u90e8\u5206\u7684\u9762\u79ef\uff0c\u8fd9\u9898\u7b54\u6848\u770b\u4e0d\u592a\u61c2
\u4e3a\u4ec0\u4e48\u4e24\u90e8\u5206\u662f\u76f8\u52a0\u4e0d\u662f\u76f8\u51cf\uff0c\u4e3a\u4ec0\u4e48\u540e\u9762\u7684\u79ef\u5206\u533a\u95f4\u662f\u03c0/2~\u03c0\u800c\u4e0d\u662f0...

\u5177\u4f53\u56de\u7b54\u5982\u56fe\uff1a

\u6269\u5c55\u8d44\u6599\uff1a
\u5f53\u52a8\u70b9\u7b26\u5408\u67d0\u4e00\u57fa\u672c\u8f68\u8ff9\u7684\u5b9a\u4e49\uff08\u5706\u3001\u692d\u5706\u3001\u76f4\u7ebf\u3001\u53cc\u66f2\u7ebf\u3001\u629b\u7269\u7ebf\uff09\u65f6\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5b9a\u4e49\uff0c\u7528\u5f85\u5b9a\u7cfb\u6570\u6cd5\u6c42\u51fa\u7cfb\u6570\uff0c\u6c42\u51fa\u52a8\u70b9\u7684\u8f68\u8ff9\u65b9\u7a0b\u3002
\u5f53\u5f62\u6210\u66f2\u7ebf\u7684\u52a8\u70b9P\uff08x\uff0cy\uff09\uff0c\u968f\u7740\u53e6\u4e00\u4e2a\u5df2\u77e5\u66f2\u7ebff\uff08x\uff0cy\uff09=0\u4e0a\u7684\u52a8\u70b9Q\uff08w\uff0cz\uff09\u6709\u89c4\u5f8b\u7684\u8fd0\u52a8\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230w=g\uff08x\uff0cy\uff09\uff0cz=h\uff08x\uff0cy\uff09\uff0c\u518d\u5229\u7528f\uff08x\uff0cy\uff09=0\u5c31\u53ef\u5f97\u5230\u66f2\u7ebf\u65b9\u7a0b\u3002
\u4e00\u4e2a\u51fd\u6570\uff0c\u53ef\u4ee5\u5b58\u5728\u4e0d\u5b9a\u79ef\u5206\uff0c\u800c\u4e0d\u5b58\u5728\u5b9a\u79ef\u5206\uff1b\u4e5f\u53ef\u4ee5\u5b58\u5728\u5b9a\u79ef\u5206\uff0c\u800c\u4e0d\u5b58\u5728\u4e0d\u5b9a\u79ef\u5206\u3002\u4e00\u4e2a\u8fde\u7eed\u51fd\u6570\uff0c\u4e00\u5b9a\u5b58\u5728\u5b9a\u79ef\u5206\u548c\u4e0d\u5b9a\u79ef\u5206\uff1b\u82e5\u53ea\u6709\u6709\u9650\u4e2a\u95f4\u65ad\u70b9\uff0c\u5219\u5b9a\u79ef\u5206\u5b58\u5728\uff1b\u82e5\u6709\u8df3\u8dc3\u95f4\u65ad\u70b9\uff0c\u5219\u539f\u51fd\u6570\u4e00\u5b9a\u4e0d\u5b58\u5728\uff0c\u5373\u4e0d\u5b9a\u79ef\u5206\u4e00\u5b9a\u4e0d\u5b58\u5728\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u66f2\u7ebf

两圆r=1,r=2cosθ交于点(1,土π/3),由对称性,
它们所围成的公共部分的面积=2(π/3-√3/4)=2π/3-√3/2.

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