求曲线y=lnx,直线x=1,y=1所围成平面图形的面积极以其绕x轴旋转一周所生成... 求曲线y=lnx与x轴及直线x=e所围平面图形面积以及绕x轴...
\u7531\u66f2\u7ebfy=lnx\u53ca\u76f4\u7ebfx+y=e+1,y=1\u6240\u56f4\u6210\u56fe\u5f62\u7684\u9762\u79ef\u7528\u4e8c\u91cd\u79ef\u5206\u8868\u793a\u4e3a\uff1f\u5176\u503c\u4e3a\uff1f\u222b\u222b_(D) dxdy
= \u222b(0\u21921) dy \u222b(e^y\u2192e+1-y) dx
= \u222b(0\u21921) [(e+1-y) - e^y] dy
= 3/2
\u5176\u5b9e\u4e09\u6761\u76f4\u7ebf\u90fd\u7ecf\u8fc7\u540c\u4e00\u70b9\u5750\u6807\uff0c\u662f\u4e0d\u662f\u9519\u6761\u4ef6\u4e86\uff1f
\u66f2\u7ebfy=lnx\u4e0ex\u8f74\u53ca\u76f4\u7ebfx=e\u6240\u56f4\u5e73\u9762\u56fe\u5f62\u9762\u79ef\u4ee5\u53ca\u7ed5x\u8f74\u65cb\u8f6c\u4e00\u5468\u6240\u5f97\u7acb\u4f53\u7684\u4f53\u79ef\u5982\u4e0b\uff1a
\u6269\u5c55\u8d44\u6599
\u4ee5\u66f2\u7ebf\u7684\u5168\u90e8\u6216\u786e\u5b9a\u7684\u4e00\u6bb5\u4f5c\u4e3a\u7814\u7a76\u5bf9\u8c61\u65f6\uff0c\u5c31\u5f97\u5230\u66f2\u7ebf\u7684\u6574\u4f53\u7684\u51e0\u4f55\u6027\u8d28\u3002\u8bbe\u66f2\u7ebfC\u7684\u53c2\u6570\u65b9\u7a0b\u4e3ar=r(s)\uff0cs\u2208\u3010\u03b1,b)\u3011\uff0cs\u4e3a\u5f27\u957f\u53c2\u6570,\u82e5\u5176\u59cb\u70b9\u548c\u7ec8\u70b9\u91cd\u5408r(\u03b1)=r(b))\uff0c\u8fd9\u65f6\u66f2\u7ebf\u662f\u95ed\u5408\u7684\uff0c\u79f0\u4e3a\u95ed\u66f2\u7ebf\u3002
\u82e5\u5b83\u5728\u8fd9\u70b9\u7684\u5207\u5411\u91cf\u91cd\u5408\uff0c\u5373r\u2521(\u03b1)=r\u2521(b))\uff0c\u4e14\u81ea\u8eab\u4e0d\u518d\u76f8\u4ea4\uff0c\u5219\u79f0\u4e3a\u7b80\u5355\u95ed\u66f2\u7ebf\u3002\u5bf9\u4e8e\u6b63\u5219\u95ed\u66f2\u7ebfC,\u628a\u5b83\u7684\u5207\u5411\u91cft(s)\u7684\u59cb\u70b9\u653e\u5728\u539f\u70b9\uff0ct(s)\u7684\u7ec8\u70b9\u8f68\u8ff9\u662f\u5355\u4f4d\u7403\u9762\u4e0a\u7684\u4e00\u6761\u95ed\u66f2\u7ebf\uff0c\u5b83\u79f0\u4e3a\u66f2\u7ebfC\u7684\u5207\u7ebf\u50cf\u6216\u5207\u7ebf\u6807\u5f62\u3002
=x(1-lnx)│<1,e>+∫<1,e>dx (应用分部积分法)
=-1+(e-1)
=e-2
绕x轴旋转一周所生成的体积=∫<1,e>π(1-ln²x)dx
=π[x(1-ln²x)│<1,e>+2∫<1,e>lnxdx] (应用分部积分法)
=π[-1+2(xlnx│<1,e>-∫<1,e>dx)] (应用分部积分法)
=π[-1+2(e-(e-1))]
=π。
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...
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绛旓細ln琛ㄧず浠ヨ嚜鐒跺鏁帮紝涔熷氨鏄互e涓哄簳鐨勫鏁 y=lnx 鍒檡'=1/x 鈭鏇茬嚎鍦▁=1澶勭殑鍒囩嚎鏂滅巼k=1/1=1 x=1甯﹀叆鏇茬嚎瑙ｅ緱锛歽=ln1=0 鎵浠ュ垏绾胯繃鐐癸紙1锛0锛夋墍浠ュ垏绾挎柟绋嬶細y=x-1
绛旓細2-x锛+ax锛庘埓h鈥(x)锛漚+1x?2锛岃繃锛1锛宧锛1锛夛級鐐圭殑鐩寸嚎鐨勬枩鐜囦负a-1锛屸埓杩囷紙1锛宧锛1锛夛級鐐圭殑鐩寸嚎鏂圭▼涓y-a=锛坅-1锛夛紙x-1锛夛紟鍙堝凡鐭ュ渾蹇冧负锛-1锛0锛夛紝鍗婂緞涓1锛岀敱棰樻剰寰梶1?a+1|(a?1)2+1锛1锛瑙ｅ緱a=1锛庯紙2锛塰鈥(x)锛漚x?2a+1x?2锛漚[x?(2?1a)]?1x?2锛...
绛旓細璇曠敤瀹氱Н鍒嗚〃绀鏇茬嚎y=lnx鐩寸嚎X=1鍜孹=2浠ュ強X杞存墍鍥存垚鐨勫钩闈㈠浘褰 鎴戞潵绛 1涓洖绛 #鐑# 浣犲彂鏈嬪弸鍦堜細浣跨敤閮ㄥ垎浜哄彲瑙佸姛鑳藉悧?姊︽兂澶╃┖灏忛晣 2016-04-16 路 TA鑾峰緱瓒呰繃459涓禐 鐭ラ亾灏忔湁寤烘爲绛斾富 鍥炵瓟閲:376 閲囩撼鐜:72% 甯姪鐨勪汉:76.3涓 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鏇村杩介棶杩界瓟...
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绛旓細杩囧師鐐逛綔鏇茬嚎y=lnx鐨勫垏绾垮彲浠ュ緱鍒 y = ln(x)锛屽洜涓鸿繖鏄竴鏉鐩寸嚎銆傜幇鍦ㄦ垜浠渶瑕佹眰鍑鸿鐩寸嚎鐨勬枩鐜囥傛枩鐜囧彲浠ラ氳繃涓ょ偣涔嬮棿鐨勫樊鍊奸櫎浠ヤ袱鐐归棿鐨勮窛绂绘潵璁＄畻锛歮 = (y2-y1)/(x2-x1)锛屽叾涓 (x1, y1) 鍜 (x2, y2) 鏄洿绾夸笂鐨勪袱涓偣銆傚湪杩欎釜渚嬪瓙涓紝鎴戜滑鍙互浣跨敤 (0,0) 鍜 (1,ln(1)) ...
绛旓細1銆佸鍥撅紝闃村奖閮ㄥ垎闈㈢Н鍗充负鎵姹傞潰绉傝繖绉嶅舰鐘剁敤y浣滀负绉垎鍙橀噺姣旇緝鏂逛究涓鐐 灏嗕袱鏉鏇茬嚎鍒嗗埆杞彉涓簓鐨勫嚱鏁帮紝鍙緱x=-y+1锛寈=e^y锛岀Н鍒嗗彉閲忎负y浠0鈫1 S闃村奖=鈭(0鈫1)(x2-x1)dy =鈭(0鈫1)[e^y-(-y+1)]dy =鈭(0鈫1)e^ydy+鈭(0鈫1)(y-1)dy =(e-1)+(0+1)=e 2銆佺敤鍒...
绛旓細绠鍗璁＄畻涓涓嬪嵆鍙紝绛旀濡傚浘鎵绀
