求三叶形曲线r=asin3t,(a>0)的面积和图形。 求三叶曲线所围图形的面积
\u9ad8\u6570\uff0c\u6c42\u66f2\u7ebf\u56f4\u6210\u7684\u9762\u79efr=asin3tS=\u222b\u222brdrdt,(r:0\u2192asin3t\uff1bt:0\u21922\u03c0)
=\u222brdr\u222bdt
=\u222b(asin3t)²/2dt
=\u03c0a²/2
\u5982\u56fe\u6240\u793a\uff1a\u4e09\u53f6\u66f2\u7ebf\u6240\u56f4\u56fe\u5f62\u7684\u9762\u79ef=0.77
如图所示，对t在[0,1/3π]范围内运用极坐标求积分，就可得到得到一个叶形面积，乘以3即可
绛旓細濡傚浘锛氬洿鎴愮殑闈㈢Н=0.38a²
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绛旓細濡傚浘锛氬洿鎴愮殑闈㈢Н=0.38a²
