考研高数极坐标下求椭圆面积，请问我哪里 椭圆面积 高数 极坐标 设x=acos y=bsin 用极坐...
\u6781\u5750\u6807\u4e0b\u79ef\u5206\u6c42\u692d\u5706\u7684\u9762\u79ef\u662f\u6211\u4e0d\u4f1a\u79ef\u5206\uff0c\u8fd8\u662f\u662f\u9519\u7684\u5982\u56fe\u6240\u793a\uff1a
\u692d\u5706\u533a\u57df\u4e00\u822c\u4e0d\u4f7f\u7528\u6781\u5750\u6807\u7684\uff0c\u56e0\u4e3ar\u7684\u4e0a\u9650\u6bd4\u8f83\u9ebb\u70e6\uff0c\u4f60\u6240\u5199\u7684\u221a(a²cos²\u03b8+b²sin²\u03b8)\u662f\u4e0d\u5bf9\u7684\u3002
\u5e94\u8be5\u662fx=rcos\u03b8\uff0cy=rsin\u03b8\uff0c\u5219\u692d\u5706\u65b9\u7a0b\u4e3a\uff1ar²cos²\u03b8/a² + r²sin²\u03b8/b² = 1
\u89e3\u5f97\uff1ar=1/\u221a(cos²\u03b8/a² + sin²\u03b8/b²)=ab/\u221a(b²cos²\u03b8 + a²sin²\u03b8)
\u5e0c\u671b\u53ef\u4ee5\u5e2e\u5230\u4f60\uff0c\u4e0d\u660e\u767d\u53ef\u4ee5\u8ffd\u95ee\uff0c\u5982\u679c\u89e3\u51b3\u4e86\u95ee\u9898\uff0c\u8bf7\u70b9\u4e0b\u9762\u7684"\u9009\u4e3a\u6ee1\u610f\u56de\u7b54"\u6309\u94ae\uff0c\u8c22\u8c22\u3002
绛旓細锛氬叾瀹炰粠妞渾鏂圭▼鍙煡锛屾き鍦嗘槸涓涓鈥滃帇缂┾濅簡鐨勫渾銆 璁炬き鍦嗘柟绋嬩负锛(x/a)^2+(y/b)^2=1 浠わ細x'=x锛寉'=y*a/b锛 鎴戜滑灏卞彲浠ュ湪鏂扮殑鍧愭爣绯讳腑寰楀埌涓涓渾锛歺'^2+y'^2=a^2 鏂板潗鏍囩郴鍏跺疄鏄竴涓湪y鏂瑰悜绛夋瘮锛堟瘮渚嬩负a/b锛夋媺闀夸簡鐨勫潗鏍囩郴锛岃繖鏍峰湪鏂板潗鏍囩郴 ...
绛旓細绗簩姝ラ敊浜锛屾き鍦嗛潰绉鐩存帴绛変簬 0鍒2蟺 鍖楁瀬鍑芥暟甯︽牴鍙风殑閭ｄ竴閮ㄥ垎 瀵硅搴︾殑绉垎锛屾病鏈変簩鍒嗕箣涓鍜岄偅涓钩鏂广
绛旓細杩欎釜瑕佺敤鍒颁簩閲嶇Н鍒嗐傚緢鏄庢樉鏈変袱涓彉閲忛渶瑕佺Н鍒嗐俽涓嶆槸涓鐩寸瓑浜巖² = (ab)²/(a²sin胃 + b²cos胃)銆備粬瑕佷粠闆跺紑濮嬪彉鍖栵紝鐒跺悗閫愭笎澧炲ぇ鍒妞渾杈圭晫銆傜Н鍒嗗緱鐢ㄦき鍦嗗煙鐨鏋佸潗鏍鏉ュ仛锛屼护x=arcos胃锛寉=brsin胃 鍥犱负s=鈭埆dxdy=鈭埆abrdrd胃 S=鈭(0->2蟺)d胃鈭(0->1...
绛旓細姹傛き鍦嗛潰绉鏈夊绉嶅姙娉 閮界畝鍗曡涓涓嬪惂 1.鎶妜^2/a^2+y^2/b^2=1鍙樺舰鍙樻垚y=f(x)鐨勫舰寮忕Н鍒嗭紝瑕佺敤杩樺師娉(浠=sint)2.瀵瑰潗鏍囩殑鏇茬嚎绉垎涓涓叕寮0.5(鈭畑dy-ydx)=鈭玠xdy=闈㈢НS 闈㈢НS=0.5(ab鈭玠t)t浠0鍒2蟺=蟺ab 3.鐢鏋佸潗鏍鐨勭Н鍒嗗叕寮忊埆(y(t))x'(t)锛屾妸x=acost,y=bsint瀵瑰簲...
绛旓細妞渾鍖哄煙涓鑸笉浣跨敤鏋佸潗鏍鐨勶紝鍥犱负r鐨勪笂闄愭瘮杈冮夯鐑︼紝浣犳墍鍐欑殑鈭(a²cos²胃+b²sin²胃)鏄笉瀵圭殑銆傚簲璇ユ槸x=rcos胃锛寉=rsin胃锛屽垯妞渾鏂圭▼涓猴細r²cos²胃/a² + r²sin²胃/b² = 1 瑙ｅ緱锛歳=1/鈭(cos²胃/a² + ...
绛旓細x=a rcost, y=b rsint, 鐩磋鍧愭爣(x,y) 鏋佸潗鏍(r,t)闈㈢Н鍏冪礌dxdy= a b r drdt闈㈢Н= t: 0-->2pi, r:0-->1 琚Н鍑芥暟鏄痑br 鐨勪簩閲嶇Н鍒 =鈭0,2蟺銆慸t鈭0,1銆慳brdr =2蟺*ab*(1/2) =蟺ab 鏈洖绛旇鎻愰棶鑰呴噰绾 宸茶禐杩 宸茶俯杩< 浣犲杩欎釜鍥炵瓟鐨勮瘎浠锋槸? 璇勮 鏀惰捣 1鏉℃姌鍙...
绛旓細閲囩敤鏋佸潗鏍囩殑闈㈢Н鍏冧负螖S =1/2 (r+螖r)^2 * 螖胃 - 1/2 r^2 * 螖胃 = r * 螖r * 螖胃锛涙墍浠鏋佸潗鏍囦笅闈㈢Н鍏紡涓篠 = 鈭埆 r dr d胃 = 鈭 1/2 r^2 d胃锛涜繖閲宺 = 1+cos胃锛涙墍浠 = 鈭 1/2 (1+cos胃)^2 d胃锛...
绛旓細浣犲皢x=r路cos胃鍜寉=r路sin胃浠ｅ叆 (x/a)^2+(y/b)^2 = 1 搴旇灏卞彲浠ユ眰鍑簉鍜屛搁棿鐨勫叧绯伙紝琛ㄧず涓簉=r(胃)鏍规嵁瀵圭О鎬э紝鍙眰绗竴璞￠檺鐨勫氨鍙互锛岀劧鍚4鍊嶃傚叿浣撹繃绋嬭緝楹荤儲锛屾噿寰楀啓浜嗭紝鑷繁缁冪粌鎵嬪惂锛
绛旓細濡傚浘鎵绀猴細
