由曲线y=lnx与x=1,x=2及x轴围成图形的面积用定积分表示A=? 试用定积分表示由曲线y=x^2,直线x=1,x=2及X轴所围...
\u7531\u66f2\u7ebfy=lnx\u4e0ex=1,x=e\u53cax\u8f74\u56f4\u6210\u56fe\u5f62\u7684\u9762\u79ef\u7528\u5b9a\u79ef\u5206\u8868\u793aA=?\u6839\u636e\u5b9a\u79ef\u5206\u7684\u51e0\u4f55\u610f\u4e49\uff0c\u76f4\u63a5\u8868\u793a\u4e58\u88ab\u79ef\u51fd\u6570\u662flnx\uff0c\u4ece1\u52302\u7684\u5b9a\u79ef\u5206
\u8ba1\u7b97\u8fd9\u4e2a\u5b9a\u79ef\u5206\u91c7\u7528\u5206\u90e8\u79ef\u5206\u6cd5\u8ba1\u7b97\uff0c\u8ba1\u7b97\u7ed3\u679c\u5982\u56fe\u6240\u793a\u662f2ln2-1
\u6240\u56f4\u6210\u5e73\u9762\u56fe\u5f62\u7684\u9762\u79ef\u7528\u79ef\u5206\u53ef\u8868\u793a\u4e3aS=\u222b(1,2)x^2dx\u3002\u8ba1\u7b97\u5f97\u51fa\u7684\u9762\u79ef\u4e3a7/3\u3002
\u89e3\uff1a\u6839\u636e\u9898\u610f\u53ef\u77e5\uff0c
\u66f2\u7ebfy=x^2\u4e0e\u76f4\u7ebfx=1\uff0cx=2\u53caX\u8f74\u56f4\u6210\u7684\u56fe\u5f62\u4e2d\uff0c
1\u2264x\u22642\uff0cdy=x^2dx\uff0c
\u90a3\u4e48\u6240\u56f4\u6210\u5e73\u9762\u56fe\u5f62\u7684\u9762\u79ef\u7528\u79ef\u5206\u53ef\u8868\u793a\u4e3a\uff0c
S=\u222b(1,2)x^2dx\uff0c
\u8ba1\u7b97\u53ef\u5f97\uff0cS=\u222b(1,2)x^2dx=7/3\u3002
\u5373\u6240\u56f4\u6210\u533a\u57df\u7684\u9762\u79ef\u4e3a7/3\u3002
\u5b9a\u79ef\u5206\u7684\u6027\u8d28
\u82e5F(x)\u4e3af(x)\u7684\u539f\u51fd\u6570\uff0c\u5219F(x)=\u222bf(x)dx\u3002\u90a3\u4e48\u222b(a,b)f(x)dx=F(b)-F(a)\u3002
\uff081\uff09a=b\u65f6\uff0c\u5219\u222b(a,a)f(x)dx=F(a)-F(a)=0\u3002
\uff082\uff09a\u2260b\u65f6\uff0c\u5219\u222b(a,b)f(x)dx=-\u222b(b,a)f(x)dx=F(b)-F(a)\u3002
\uff083\uff09\u222b(a,a)k*f(x)dx=k*\u222b(a,b)f(x)dx=k*\uff08F(b)-F(a)\uff09\u3002\uff08\u5176\u4e2dk\u4e3a\u4e0d\u4e3a\u96f6\u7684\u5e38\u6570\uff09
\u5b9a\u79ef\u5206\u7684\u5e94\u7528
\uff081\uff09\u89e3\u51b3\u6c42\u66f2\u8fb9\u56fe\u5f62\u7684\u9762\u79ef\u95ee\u9898\u3002
\uff082\uff09\u6c42\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u7684\u8def\u7a0b\u3002
\u505a\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u7684\u7269\u4f53\u7ecf\u8fc7\u7684\u8def\u7a0bs\uff0c\u7b49\u4e8e\u5176\u901f\u5ea6\u51fd\u6570v=v(t) (v(t)\u22650)\u5728\u65f6\u95f4\u533a\u95f4[a,b]\u4e0a\u7684\u5b9a\u79ef\u5206\u3002
\uff083\uff09\u53d8\u529b\u505a\u529f\u3002
\u67d0\u7269\u4f53\u5728\u53d8\u529bF=F(x)\u7684\u4f5c\u7528\u4e0b\uff0c\u5728\u4f4d\u79fb\u533a\u95f4[a,b]\u4e0a\u505a\u7684\u529f\u7b49\u4e8eF=F(x)\u5728[a,b]\u4e0a\u7684\u5b9a\u79ef\u5206\u3002
绛旓細A = 鈭 lnx dx (1鈫抏) = xlnx (1鈫抏) - 鈭 dx (1鈫抏) = elne - 1ln1 - (e - 1) = 1
绛旓細鏍规嵁瀹氱Н鍒嗙殑鍑犱綍鎰忎箟锛岀洿鎺ヨ〃绀轰箻琚Н鍑芥暟鏄lnx锛屼粠1鍒2鐨勫畾绉垎 璁＄畻杩欎釜瀹氱Н鍒嗛噰鐢ㄥ垎閮ㄧН鍒嗘硶璁＄畻锛岃绠楃粨鏋滃鍥炬墍绀烘槸2ln2-1
绛旓細A = 鈭 lnx dx (1鈫抏) = xlnx (1鈫抏) - 鈭 dx (1鈫抏) = elne - 1ln1 - (e - 1) = 1
绛旓細2014-11-22 璇曠敤瀹氱Н鍒嗚〃绀虹敱鏇茬嚎y=x^2,鐩寸嚎x=1,x=2鍙奨杞存墍鍥... 4 2012-06-12 璇曠敤瀹氱Н鍒嗚〃绀虹敱鏇茬嚎y=cosx涓庣洿绾縳=1,x=3/2鍙妜... 2016-07-01 姹傜敱鏇茬嚎y=1/x鍜岀洿绾縴=x,x=2鎵鍥存垚鐨勫钩闈㈠浘褰㈢殑闈㈢Н 486 2013-01-03 鐢辨洸绾縴=lnx涓巟=1,x=e鍙妜杞村洿鎴愬浘褰㈢殑闈㈢Н鐢ㄥ畾绉垎... 2012-...
绛旓細瑙ｏ細鈭垫洸绾挎柟绋嬩负y=lnx 鈭鏇茬嚎涓鐩寸嚎 x=1锛寈=2锛屽強x杞村洿鎴愮殑鍥惧舰鐨 闈㈢НA=鈭 (1锛2) lnxdx 鈭存湁A=(xlnx-x)|(1锛2)=2ln2-1 涓鑸畾鐞 瀹氱悊1锛氳f(x)鍦ㄥ尯闂碵a,b]涓婅繛缁紝鍒檉(x)鍦╗a,b]涓婂彲绉傚畾鐞2锛氳f(x)鍖洪棿[a,b]涓婃湁鐣岋紝涓斿彧鏈夋湁闄愪釜闂存柇鐐癸紝鍒檉(x)鍦╗a,b]涓...
绛旓細1) 鈭<1,e>lnxdx=[xlnx-x]|<1,e>=1.2) 缁晉杞 V1=鈭<1,e>蟺y²dx =蟺鈭<1,e>ln²xdx =蟺[xln²x]|<1,e>-蟺鈭<1,e>2lnxdx =蟺(e-2).3) 缁晊杞 V2=鈭<0,1>蟺x²dy =鈭<0,1>蟺e^2ydy =蟺/2e^2y|<0,1> =蟺/2(e²-1...
绛旓細瑙ｏ細鎵鍥存垚骞抽潰鍥惧舰鐨勯潰绉=鈭<1,e>(1-lnx)dx =x(1-lnx)鈹<1,e>+鈭<1,e>dx (搴旂敤鍒嗛儴绉垎娉)=-1+(e-1)=e-2 缁晉杞存棆杞竴鍛ㄦ墍鐢熸垚鐨勪綋绉=鈭<1,e>蟺(1-ln²x)dx =蟺[x(1-ln²x)鈹<1,e>+2鈭<1,e>lnxdx] (搴旂敤鍒嗛儴绉垎娉)=蟺[-1+2(xlnx鈹<1,...
绛旓細鍥炵瓟锛氬彧瑕佺瓟妗堝悧
绛旓細y=x鐨勫浘鍍忎笌y=lnx鐨勫浘鍍忔槸娌℃湁浜ょ偣鐨勶紝涓よ呭苟涓嶄細鐩镐氦銆傚嚱鏁帮細鍏朵腑y=x鐨勫嚱鏁板浘鍍忔槸涓鏉¤繃鍘熺偣鐨勭洿绾匡紝鍥惧儚缁忚繃涓銆佷笁璞￠檺锛屽苟涓旀槸涓銆佷笁璞￠檺鐨勮骞冲垎绾匡紝鍑芥暟鍥惧儚鍦ㄦ暣涓畾涔夊尯闂村崟璋冮掑銆傝寉=lnx鐨勫嚱鏁板浘鍍忔槸涓鏉¤繃鐐癸紙1,0锛夌殑鏇茬嚎锛屽叾瀹氫箟鍩熶负锛0锛+鈭烇級锛屽湪x=1鏃讹紝y=lnx鐨勫嚱鏁板浘鍍忎笌y=...
绛旓細瑙ｏ細鍥犱负鍑芥暟y=x+lnx鍗曞锛屼笖褰x=1鏃秠=1>0锛屾墍浠ユ骞抽潰鍥惧舰鐨勯潰绉负 ʃ(1鍒癳)(x+lnx)dx 锛(x²/2+xlnx-x)|(1鍒癳)锛(e²/2+e-e)-(1/2+0-1)锛(e²+1)/2.
