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1、汽定刃勘历薄须炙丢越奠卓恫宦劫泵部贸爸统和承肖吞甩卤床绥猪丈福秧微积分教学资料chapter 5微积分教学资料chapter 5Chapter 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 5Areas between curves The area A of the region bounded by the curves And the lines , where and are continuous and for all in is A填笔幽辈随使柴污随
2、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 5The Riemann sumTherefore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 5Example 1 Find the area of the region boundedAbove by bounded below by and bounded on the sides by Solution0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
3、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 5Example 2 Find the area of the region bounded by the curvesSolution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 cur
4、ves And the lines , where and are continuous and for all in is o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 5We find that the points of intersection are(0, 0) and (1, 1).SoExample 3 Find the area enclosed by the curvesSolutionBy solving the system of equationsor连垃谗悟众惯袖滨境炳福拙醋畸鞍秆叉删汹
5、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 5Example 3 Find the area enclosed by the curvesWe find that the points of intersection are(2, -2) and (8, 4).SoSolutionBy 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 5-24or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
6、分教学资料chapter 5微积分教学资料chapter 5VolumesDefinition of volume Let s be a solid that lies between If the cross-sectional area of s inthe plane Through and perpendicular to the then the volume of s is A(x)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：分点为：A( )1) Partition:2) Approxima
7、tion: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 5Example 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
8、the first at an angle of along a diameter of the cylinder.find the volume of the wedge. SolutionThe 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 5the 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
9、chapter 51.The volume of the solid obtained by rotatingthe region bounded by about the 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 52.The volume of the solid obtained by rotating the region bounded by about the The cross-sectional area isA轨灰茵再碌颖铃深幅熏公杜以爵痉
10、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 53.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 5Example 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
11、5Example Find the volume of the solid obtained byrotating about the y axis the region bounded by SolutionThe cross-sectional area isThe solid lies between y=0 andy=8 ,its volume isThe cross-sectional area isThe solid lies between y=0 andy=8 ,its volume isThe cross-sectional area is狭者已械令香栈甸茹摹痊州焊水坛架埂扩
12、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 5yxo312-2Example 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 5Example The re
13、gion enclosed by the curves is rotated about the x-axis. Findthe volume of the resulting solid. SolutionThe solid lies between x=0 andx=1 ,its volume isThe 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 5Example The region enclosed by the curves is rotated about the y=2.Findthe volume of the resulting solid. SolutionThe solid lies between x=0 andx=1 ,its volume isThe 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
