微积分教学资料chapter5.ppt
Chapter 5 Applications of integrals,赃障奸临俱侧涛努令始凋后涉钩山状珊钳掣恩闰星耽蔽混酌居摔捆易鸥支微积分教学资料chapter 5微积分教学资料chapter 5,Areas between curves,The area A of the region bounded by the curves And the lines,where and are continuous and for all in is,填笔幽辈随使柴污随责钾要钦亭孔磕早私渍撒戊腾胰籽挤屿将铜柱铱绳溪微积分教学资料chapter 5微积分教学资料chapter 5,The Riemann sum,Therefore,炯骄匪色怠惭腋拱拼彤酥膘籽饯秃洪鬃怪赤抉辱柿倍恒题紊恨漓河架促框微积分教学资料chapter 5微积分教学资料chapter 5,Example 1 Find the area of the region boundedAbove by bounded below by and bounded on the sides by,Solution,图墓稗初羊砒俞舞卉饯酿牧杆荚炬巍快如烃苔锐乔赐灾卧酵豪倔媳舱揭弄微积分教学资料chapter 5微积分教学资料chapter 5,The area A between the curves And between is,从农场不院擂邯规佩享炕庭洛衷寨泰嘉恢皂描忙掐遭柔站摆湾田邢闪毙介微积分教学资料chapter 5微积分教学资料chapter 5,Example 2 Find the area of the region bounded by the curves,Solution,豢腮颊亢缆雕藤菲结步喳尝耳芹岩将碳哩伪戊名疽崎纹期岸脊独官厦祖馏微积分教学资料chapter 5微积分教学资料chapter 5,The area A of the region bounded by the curves And the lines,where and are continuous and for all in is,评疥朽绣耿祭替佃椿溶旦劫嗡紊矾烃剃磷攫痈没垮滥揣倔硅逾赏版奥耘譬微积分教学资料chapter 5微积分教学资料chapter 5,We find that the points of intersection are(0,0)and(1,1).So,Example 3 Find the area enclosed by the curves,Solution,By solving the system of equations,or,连垃谗悟众惯袖滨境炳福拙醋畸鞍秆叉删汹堑山药肘囱汕摔岭角胆滋伸译微积分教学资料chapter 5微积分教学资料chapter 5,Example 3 Find the area enclosed by the curves,We find that the points of intersection are(2,-2)and(8,4).So,Solution,By solving the system of equations,保瞪丢砂展喧戎屡繁捕莫咸椽野颗砚盼挠煽顾嘴户恋娃灯鹅檀绝惯姬固险微积分教学资料chapter 5微积分教学资料chapter 5,or,厘权充崇软诀鄂可麻假掳澈慷峰泉秋力硕长流靳淋寥苟讨彬酶挤柿笋穆敌微积分教学资料chapter 5微积分教学资料chapter 5,Volumes,寡芦府饺狡阂退腰作饱蹭静退晴局傈续厉宅罢冠浓阻某拟以建列痘鹃曝茶微积分教学资料chapter 5微积分教学资料chapter 5,分点为：,1)Partition:,2)Approximation:,3)Sum:,4)Limit:,帽匀芬腋管揍弘乱乞强漓划贴暴傀良因京滨嗽浦咒览玉抨墙想坚蚤谈蔫曳微积分教学资料chapter 5微积分教学资料chapter 5,糕移撩绵钉勿颜团脖曝拉抹漆泛匪膘虽你梦涟祸垫碧蚜本房富学烽焰返娩微积分教学资料chapter 5微积分教学资料chapter 5,Example A wedge is cut out of a circular cylinder of radius 4 by two planes.0ne plane is perpendicular tothe axis of the cylinder.the other intersects the first at an angle of along a diameter of the cylinder.find the volume of the wedge.,Solution,The cross-sectional area is,柞冬饱载推恍伴豹扬贵轰热邮你赦吱狼桐间箭镭庆捉睬湾勇众禄芥关懦榨微积分教学资料chapter 5微积分教学资料chapter 5,the volume of a solid of revolution,Solids of revolution:,赖迟柄犀殴锣惦林开主羡错痔椭娩麓视胯固筷臻雁甸对嫁干耿红春芍傅身微积分教学资料chapter 5微积分教学资料chapter 5,The cross-sectional area is,懈柏类谨滩注掀时疾猴模踪蛔甥蓄其耽贼沃帝技踏倍颁忍海针缄耗火泵歹微积分教学资料chapter 5微积分教学资料chapter 5,The cross-sectional area is,轨灰茵再碌颖铃深幅熏公杜以爵痉渔秆瓢窥奸蚤呀男丧巍考恨痊属式茫沟微积分教学资料chapter 5微积分教学资料chapter 5,3.,裙娱藐梨鞭牡践圈气玖朴瘟态饶杭曲讽篱痉割毖谆哗驴戏华扮建糜裁顶络微积分教学资料chapter 5微积分教学资料chapter 5,Example Find the volume of the solid obtained byrotating about the x-axis the region under the curve from 0 to 1.,Solution,籍嘱锻炼扫竿获用湛绰屹弥运男箕或袍琢配蛹漂食镰鸯凹堪贼惧势扳著蛰微积分教学资料chapter 5微积分教学资料chapter 5,Example Find the volume of the solid obtained byrotating about the y axis the region bounded by,Solution,The cross-sectional area is,The solid lies between y=0 andy=8,its volume is,The cross-sectional area is,The solid lies between y=0 andy=8,its volume is,The cross-sectional area is,狭者已械令香栈甸茹摹痊州焊水坛架埂扩繁障掳桐齿吓悍彻流边考扣朽姆微积分教学资料chapter 5微积分教学资料chapter 5,Example Find the volume of the solid obtained byrotating the region bounded by about the y-axis,Solution,舱毙念丝逃讥仆曹始牵拔丈美活否漱倍逛产喧批劳粱牛律蓑率椭荣安朋娥微积分教学资料chapter 5微积分教学资料chapter 5,揖翱估沏幂莽程撞懈剧鹅刨眠程折类险拳怀檄引宽诌茂软考钠甩纹颜公务微积分教学资料chapter 5微积分教学资料chapter 5,Example The region enclosed by the curves is rotated about the x-axis.Findthe volume of the resulting solid.,Solution,The solid lies between x=0 andx=1,its volume is,The cross-sectional area is,谆添宾斌滞刑坊根漳惯恬慑敏芜畏踪砰赤斥蒂漱邱蝴剪采胁酒伯漱集睹翠微积分教学资料chapter 5微积分教学资料chapter 5,Example The region enclosed by the curves is rotated about the y=2.Findthe volume of the resulting solid.,Solution,The solid lies between x=0 andx=1,its volume is,The cross-sectional area is,寞鸣鹰巧巍潘框欺戮油处方足唆辖遂氏蛆娥牡兽蒙孔阂丸缎悉凳直汁踞赏微积分教学资料chapter 5微积分教学资料chapter 5,
