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
它们所围成的公共部分的面积=2（π/3-√3/4）=2π/3-√3/2.
绛旓細鏇茬嚎r=2½sin胃涓巖²=cos2胃鎵鍥存垚鍥惧舰闈㈢Н涓猴細pi/6+(1-鈭3)/2銆傝В锛氭湰棰樺埄鐢ㄤ簡瀹氱Н鍒嗙殑鎬ц川姹傝В銆傚洜涓簉=鈭2sin胃琛ㄧず鍦嗭紝涓斿渾蹇冨湪鐐(鈭2/2,pi/2)澶勶紝鍗婂緞涓衡垰2/2銆俽^2=cos2胃,琛ㄧず鍙岀航绾裤傚張鏈夋瀬瑙捨歌寖鍥存槸[-pi,-3pi/4],[-pi/4,pi/4],[3pi/4,pi]鍐嶈仈绔嬩袱...
绛旓細濡傚浘鎵绀猴細鎵鍥存垚鐨勫浘褰㈠湪蟻=1鍐呯殑闈㈢Н涓1.31
绛旓細璁＄畻鐨勫彧鏄孩鑹查儴鍒嗛潰绉細涓(1/2)蟺a²濡傛灉瑕佹眰鐨勯潰绉槸r 鈮 a(1 + cos胃)锛宺 鈮 2acos胃閮ㄥ垎鐨勮瘽 杩欏崟鐙槸r = 2acos胃鍥存垚鐨勯潰绉紝涓合a²锛屽洜涓哄績褰㈢嚎鎶婅繖鏁翠釜鍦嗗舰閮藉寘鍥村湪鍐呫
绛旓細鍖呮嫭鐩寸嚎銆佹姌绾裤佺嚎娈点佸渾寮х瓑銆 澶勫杞姌鐨勬洸绾夸竴鑸叿鏈夋棤绌峰ぇ鐨勯暱搴﹀拰闆剁殑闈㈢Н锛岃繖鏃锛屾洸绾鏈韩灏辨槸涓涓ぇ浜1灏忎簬2缁寸殑绌洪棿銆傚井鍒嗗嚑浣曞鐮旂┒鐨勪富瑕佸璞′箣涓銆傛洸绾垮彲鐪嬫垚绌洪棿璐ㄧ偣杩愬姩鐨勮建杩广傛洸绾跨殑鏇翠弗鏍肩殑瀹氫箟鏄尯闂次憋紝b)鍒癊3涓殑鏄犲皠r:伪,b)E3銆傛湁鏃朵篃鎶婅繖鏄犲皠鐨勫儚绉颁负鏇茬嚎銆
绛旓細r^2=r+rcose x^2+y^2=鈭(x^2+y^2)+x 杩欐牱灏卞寲鎴愪簡銆傦紙璁颁綇4涓叕寮忥細r^2=x^2+y^2銆乼ane=y/x銆亁=rcose銆亂=rsine銆)鍦ㄤ袱鐐归棿鐨勫叧绯荤敤澶硅鍜岃窛绂诲緢瀹规槗琛ㄧず鏃讹紝鏋佸潗鏍囩郴渚挎樉寰楀挨涓烘湁鐢紱鑰屽湪骞抽潰鐩磋鍧愭爣绯讳腑锛岃繖鏍风殑鍏崇郴灏卞彧鑳戒娇鐢ㄤ笁瑙掑嚱鏁版潵琛ㄧず銆傚浜庡緢澶氱被鍨嬬殑鏇茬嚎锛鏋佸潗鏍囨柟绋...
绛旓細(x-a)²+(y-a)²=r² 鎵琛ㄧず鐨鏇茬嚎鏄互O(a锛宐)涓哄渾蹇冿紝浠涓哄崐寰勭殑鍦嗭紱x²+y²+Dx+Ey+F=0鎵琛ㄧず鐨勬洸绾挎槸浠(-D/2锛-E/2)涓哄渾蹇冿紝浠 涓哄崐寰勭殑鍦嗐4銆佷笁瑙掑嚱鏁板熀鏈叕寮忋俿in²胃+cos²胃=1 sec²胃-tan²胃=1 csc²胃-...
绛旓細鍏蜂綋鍥炵瓟濡傚浘锛
绛旓細{ r = 1 + cos胃{ r = 1浜ょ偣(r,胃)涓篬1,蟺/2]鍜孾- 1,- 蟺/2]闈㈢Н = 2鈭玔0鈫捪/2] (1/2)(1)² d胃 + 2鈭玔蟺/2鈫捪] (1/2)(1 + cos胃)² d胃= [蟺/2] + [3蟺/4 - 2]= 5蟺/4 - 2= (5蟺 - 8)/4 ...
绛旓細鍒嗘瀽锛氬厛灏嗗師鏋佸潗鏍囨柟绋嬩袱杈瑰悓涔樹互r鍚庡寲鎴愮洿瑙掑潗鏍囨柟绋嬶紝鍐嶅埄鐢ㄧ洿瑙掑潗鏍囨柟绋嬭繘琛屾眰瑙ｉ潰绉嵆鍙傝В娉曪細r²=2arcos胃锛鍖栦负x²+y²=2ax锛屽嵆锛歺²-2ax+a²+y²=a²锛岋紙x-a锛²+y²=a²锛岃繖鏄涓涓渾锛屽叾鍗婂緞涓篴锛岄潰绉疭 = 蟺 a...
绛旓細浠涔堟椂鍊欏彲鐢ㄦ暟瀛楄〃绀哄彇鍊艰寖鍥达紝浠涔堟椂鍊欑敤涓夎鍑芥暟琛ㄧず鍙栧艰寖鍥淬傝鏍规嵁瀹為檯鎯呭喌鏉ュ晩锛屽尯鍩熺殑琛ㄨ揪寮忎腑鏄暟瀛楀氨鐢ㄦ暟瀛楋紝鏄笁瑙掑嚱鏁板氨鐢ㄤ笁瑙掑嚱鏁帮紝銆倄²+y²鈮2x鍗 (rsin胃)²+锛坮cos胃锛²=2rcos胃 鍖栫畝寰楄竟鐣鏇茬嚎涓r=2cos胃銆傦紙鑷繁鐢诲浘锛屾瀬鐐瑰湪鍖哄煙鍐咃級鎵浠ユ墍绉尯鍩熸槸0鈮...
