平面x=0,y=0由,z=0,x+y=2,3x+2y+z=6所围成的闭区域 1、设d是由x=0,y=0,x+y=1所围成的闭区域,则∫∫...

\u7531\u5e73\u9762x=0,y=0,z=0\u548cx+2y+3z=1\u56f4\u6210\u7684\u7a7a\u95f4\u7acb\u4f53\u5728Xoy\u9762\u4e0a\u7684\u6295\u5f71\u533a\u57df\u4e3a\u591a\u5c11\uff1f

\u8fd9\u4e2a\u7a7a\u95f4\u7acb\u4f53\u6295\u5f71\u5728x0y\u9762\u4e0a\u4e3a\u4e00\u4e2a\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cS=½\u00d71\u00d7½=¼

\u89e3\u9898\u8fc7\u7a0b\u5982\u4e0b\u56fe\uff1a

\u6269\u5c55\u8d44\u6599\u6c42\u51fd\u6570\u79ef\u5206\u7684\u65b9\u6cd5\uff1a
\u5982\u679c\u4e00\u4e2a\u51fd\u6570f\u5728\u67d0\u4e2a\u533a\u95f4\u4e0a\u9ece\u66fc\u53ef\u79ef\uff0c\u5e76\u4e14\u5728\u6b64\u533a\u95f4\u4e0a\u5927\u4e8e\u7b49\u4e8e\u96f6\u3002\u90a3\u4e48\u5b83\u5728\u8fd9\u4e2a\u533a\u95f4\u4e0a\u7684\u79ef\u5206\u4e5f\u5927\u4e8e\u7b49\u4e8e\u96f6\u3002\u5982\u679cf\u52d2\u8d1d\u683c\u53ef\u79ef\u5e76\u4e14\u51e0\u4e4e\u603b\u662f\u5927\u4e8e\u7b49\u4e8e\u96f6\uff0c\u90a3\u4e48\u5b83\u7684\u52d2\u8d1d\u683c\u79ef\u5206\u4e5f\u5927\u4e8e\u7b49\u4e8e\u96f6\u3002
\u4f5c\u4e3a\u63a8\u8bba\uff0c\u5982\u679c\u4e24\u4e2a \u4e0a\u7684\u53ef\u79ef\u51fd\u6570f\u548cg\u76f8\u6bd4\uff0cf\uff08\u51e0\u4e4e\uff09\u603b\u662f\u5c0f\u4e8e\u7b49\u4e8eg\uff0c\u90a3\u4e48f\u7684\uff08\u52d2\u8d1d\u683c\uff09\u79ef\u5206\u4e5f\u5c0f\u4e8e\u7b49\u4e8eg\u7684\uff08\u52d2\u8d1d\u683c\uff09\u79ef\u5206\u3002
\u51fd\u6570\u7684\u79ef\u5206\u8868\u793a\u4e86\u51fd\u6570\u5728\u67d0\u4e2a\u533a\u57df\u4e0a\u7684\u6574\u4f53\u6027\u8d28\uff0c\u6539\u53d8\u51fd\u6570\u67d0\u70b9\u7684\u53d6\u503c\u4e0d\u4f1a\u6539\u53d8\u5b83\u7684\u79ef\u5206\u503c\u3002\u5bf9\u4e8e\u9ece\u66fc\u53ef\u79ef\u7684\u51fd\u6570\uff0c\u6539\u53d8\u6709\u9650\u4e2a\u70b9\u7684\u53d6\u503c\uff0c\u5176\u79ef\u5206\u4e0d\u53d8\u3002
\u5bf9\u4e8e\u52d2\u8d1d\u683c\u53ef\u79ef\u7684\u51fd\u6570\uff0c\u67d0\u4e2a\u6d4b\u5ea6\u4e3a0\u7684\u96c6\u5408\u4e0a\u7684\u51fd\u6570\u503c\u6539\u53d8\uff0c\u4e0d\u4f1a\u5f71\u54cd\u5b83\u7684\u79ef\u5206\u503c\u3002\u5982\u679c\u4e24\u4e2a\u51fd\u6570\u51e0\u4e4e\u5904\u5904\u76f8\u540c\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u79ef\u5206\u76f8\u540c\u3002\u5982\u679c\u5bf9 \u4e2d\u4efb\u610f\u5143\u7d20A\uff0c\u53ef\u79ef\u51fd\u6570f\u5728A\u4e0a\u7684\u79ef\u5206\u603b\u7b49\u4e8e\uff08\u5927\u4e8e\u7b49\u4e8e\uff09\u53ef\u79ef\u51fd\u6570g\u5728A\u4e0a\u7684\u79ef\u5206\uff0c\u90a3\u4e48f\u51e0\u4e4e\u5904\u5904\u7b49\u4e8e\uff08\u5927\u4e8e\u7b49\u4e8e\uff09g\u3002
\u5982\u679c\u5728\u95ed\u533a\u95f4[a,b]\u4e0a\uff0c\u65e0\u8bba\u600e\u6837\u8fdb\u884c\u53d6\u6837\u5206\u5272\uff0c\u53ea\u8981\u5b83\u7684\u5b50\u533a\u95f4\u957f\u5ea6\u6700\u5927\u503c\u8db3\u591f\u5c0f\uff0c\u51fd\u6570f\u7684\u9ece\u66fc\u548c\u90fd\u4f1a\u8d8b\u5411\u4e8e\u4e00\u4e2a\u786e\u5b9a\u7684\u503cS\uff0c\u90a3\u4e48f\u5728\u95ed\u533a\u95f4[a,b]\u4e0a\u7684\u9ece\u66fc\u79ef\u5206\u5b58\u5728\uff0c\u5e76\u4e14\u5b9a\u4e49\u4e3a\u9ece\u66fc\u548c\u7684\u6781\u9650S\u3002

如图所示：

骞抽潰x=0,y=0鐢,z=0,x+y=2,3x+2y+z=6鎵鍥存垚鐨勯棴鍖哄煙
绛旓細濡傚浘鎵绀猴細

鐢骞抽潰x=0,y=0,z=0,x=1,y=1鍙
绛旓細鐢卞洓涓骞抽潰x=0,y=0,x=1,y=1鎵鏋勬垚鍥惧舰涓庡钩闈+y+z=7鐨勪氦鐐逛负锛0,0,7锛夛紙0,1,6锛夛紙1,1,5锛夛紙1,0,6锛変綋绉=搴曢潰绉箻楂=1*锛7+6+5+6锛/4=6

璁＄畻鈭埉xyzdS,鍏朵腑危涓虹敱骞抽潰x=0,y=0,z=0鍙妜+y+z=1鎵鍥存垚鐨勫洓闈綋鐨...
绛旓細瑙ｆ瀽濡備笅锛氱涓鍨嬫洸闈㈢Н鍒嗙墿鐞嗘剰涔夋潵婧愪簬瀵圭粰瀹氬瘑搴﹀嚱鏁扮殑绌洪棿鏇查潰锛岃绠楄鏇查潰鐨勮川閲忋傜浜屽瀷鏇查潰绉垎鐗╃悊鎰忎箟鏉ユ簮瀵逛簬缁欏畾鐨勭┖闂存洸闈㈠拰娴佷綋鐨勬祦閫燂紝璁＄畻鍗曚綅鏃堕棿娴佺粡鏇查潰鐨勬绘祦閲忋傞櫎鏁版槸灏忔暟鐨勫皬鏁伴櫎娉曟硶鍒欙細1锛夊厛鐪嬮櫎鏁颁腑鏈夊嚑浣嶅皬鏁帮紝灏辨妸琚櫎鏁扮殑灏忔暟鐐瑰悜鍙崇Щ鍔ㄥ嚑浣嶏紝鏁颁綅涓嶅鐨勭敤闆惰ˉ瓒炽2锛夌劧鍚庢寜鐓...

搴旂敤涓夐噸绉垎璁＄畻鏈骞抽潰X=0,y=0,z=0鍙妟=2x+y+2鎵鍥存垚鐨勫洓闈綋鐨勪綋绉
绛旓細褰x=0,y=0,z=2;x=0,z=0,y=-2;y=0,z=0,x=-1;v=1/3 脳 2 脳 2 脳 1 = 4/3

姹傜敱鍧愭爣闈=0,y=0,z=0,鍙妜/a+y/b+z/c=1鎵鍥寸殑浣撶Н
绛旓細缁欏嚭鐨勮В绛旀槸姹傛墍鍥存洸闈锛堝钩闈級鐨勯潰绉 涓婇檺琛ㄧず锛骞抽潰 x/a+y/b+z/c = 1 鍦 xOy 鍧愭爣骞抽潰涓婃姇褰憋細 x/a+y/b = 1 鍗 y = b - bx/a 灏辨槸绾㈢嚎澶勪笂闄愯〃绀恒

姹傜敱骞抽潰x=0,y=0,x+y=1鎵鍥村煄鐨勬煴闈㈣骞抽潰z=0,鍙婃姏鐗╅潰x²+y²...
绛旓細(2)x锛0~1,y锛0~1鏄釜姝ｆ柟褰㈢殑鏌遍潰(3)y锛3z锛屾槸涓繃x杞寸殑鏂滈潰锛屽叾鍜屾姏鐗╅潰鐨勪氦绾垮湪xoy涓婄殑鎶曞奖鏄細x²锛媦²锛4锛峺/3璇ユ姇褰辨槸涓渾锛屽苟涓斿寘鍚簡鍓嶉潰绗(2)鏉℃墍璇寸殑姝ｆ柟褰(4)鏍规嵁涓婅堪鍒嗘瀽锛屾墍姹傚嚑浣曚綋瀹為檯灏辨槸鎶涚墿闈箣涓嬶紝鏂滈潰涔嬩笂鐨勭┖闂磋姝ｆ柟褰㈡煴闈㈡墍鎴殑浣撶Н銆俈锛濃埆[0,1...

...鈭戔埆鈭笂绉垎xyzdS,鍏朵腑鈭戞槸鐢骞抽潰x=0,y=0,z=0鍙妜+y+z=1鎵鍥存垚鐨...
绛旓細鍦ㄢ垜1 鈭2 鈭3涓婏紝鍒嗗埆婊¤冻x=0, y=0, z=0 鎵浠xyz=0 鎵浠モ埆鈭玿yzdS=鈭埆0dS=0 鍘熺Н鍒=[鈭(0->1) xdx] *[鈭(0->x) y^2dy] *[鈭(0->xy) z^3dz]=1/364 鍦ㄥ嚑浣曚笂 涓庣幆闈紙#T锛夌殑杩炴帴鍔犱笂涓涓墜鏌勶紝涓ょ杩炴帴鍦ㄨ〃闈㈢殑鍚屼竴渚э紝鑰屼笌鍏嬭幈鎭╃摱锛#K锛夌殑杩炴帴鍔犱笂鎵嬫焺锛屼袱绔...

鈭xzdxdy+xydydz+yzdzdx,鈭戜负骞抽潰x=o,y=0,z=0,x+y+z=1鎵鍥存垚鐨
绛旓細鎵浠モ埆鈭xydydz+yzdzdx+xzdxdy= -鈭埆yzdzdx,鍖栦负浜岄噸绉垎,绉垎闈负宸︿晶闈,甯﹀叆y=0,鍐嶈绠梮+y+z=1闈笂鐨勭Н鍒,鐢变簬杞崲瀵圭О鎬,鍦ㄨ绉垎闈笂鈭埆xydydz=鈭埆yzdzdx=鈭埆xzdxdy銆傚垯鈭埆xydydz+yzdzdx+xzdxdy=3鈭埆xzdxdy 鐢变簬瀹氬悜涓烘鍚,鍒欑敱1-x-y=z甯﹀叆寰椾簩閲嶇Н鍒嗐3鈭埆xzdxdy...

姹骞抽潰x=0,y=0,x+y=1鎵鍥存垚鐨勬煴浣,琚骞抽潰z=0鍙婂钩闈²+y²=6-z...
绛旓細xy骞抽潰鍐呯殑鐩寸嚎锛x=0锛寉=0锛y=1- x 鎵鍥存垚涓涓笁瑙掑舰鍖哄煙锛涙洸椤舵煴浣撲笅搴曢潰锛歺y骞抽潰锛 涓婂簳闈㈡槸锛z=6- x² - y²鎵浠ワ紝浣撶Н锛歏=鈭埆D[6- x² - y²]dxdy=鈭<0,1>dx鈭<0,1-x>[6- x² - y²]dy =鈭<0,1>dx[6y- x²y -...

姹傝В杩欓亾楂樻暟棰,鎶曞奖鍖哄煙D
绛旓細x=0锛寉=0锛寊=0灏辨槸yoz,xoz,xoy涓変釜闈紝骞抽潰x+2y+3z=1鍦▁oy闈笂鐨z=0锛鎶曞奖涓簒+2y=1锛屾墍浠ユ姇褰卞尯鍩熶负锛歺oy骞抽潰涓庣洿绾縳+2y=1鎵鍥村尯鍩

扩展阅读：平面y+z=0 ... 平面z=0 ... 函数图像生成器app ... 求解方程计算器 ... x=0是方程吗 ... 平面x=y ... x+y+z=0的图像 ... x=y^2 ... !(x=a)&&(y=b)&&0详细 ...