高等数学-一元积分学-定积分的应用

高等数学-一元积分学-定积分的应用

几何应用

求面积体积

例1
image-20200502000848670

\(L : y=\sqrt{x-1}\) 1) 求曲线上的切线,且该切线过原点 2) 求曲线、切线、x轴所夹图形的面积 3) 所夹图形绕x轴旋转一周形成的图形的体积

image-20200502000955372
image-20200502001142899
image-20200502001349125
image-20200502001514639
例2

1)求摆线第一拱的面积 2)摆线第一拱绕x轴旋转一周形成图形的体积

image-20200502004215531
image-20200502004300550
image-20200502004519452
image-20200502004640486
例3
image-20200502004746608
例4
image-20200502004851139
例5
image-20200503162329535
image-20200503162400622
image-20200503162436990
例6
image-20200503195524460
image-20200503195656893
例7
image-20200503202823319
image-20200503204103337
image-20200503204145282
例8
image-20200503224911756
image-20200503225229388
例9
image-20200503225926801
例10
image-20200505175756028
image-20200505175743687
例11
image-20200505220808540
image-20200505220740301
例12
image-20200505222551355
image-20200505222532742
例13
image-20200508223637226
image-20200508223731369
image-20200508223619295
例14
image-20200508225342070
image-20200508225327824
例15
image-20200508230030524
image-20200508230005684
例16
image-20200508231241231
image-20200508231226651
例17
image-20200511135002879
image-20200511134940465
例18
image-20200511140558087
image-20200511140533596
例19
image-20200511150208005
image-20200511150230262
例20
image-20200511154214348
image-20200511154233324
例21
image-20200511165911131
image-20200511165855226
例22
image-20200511171329849
image-20200511171306058
例23
image-20200511172027585
image-20200511171955794
image-20200511172010771
例24
image-20200511180658728
image-20200511180730657
例25
image-20200511201758979
image-20200511201827919
例26
image-20200511212157990
image-20200511212214391
例27
image-20200511213746835
image-20200511213728683

已知面积条件求函数或参数

例1
image-20200511152811348
image-20200511152822324
image-20200511152738831
image-20200511152751831
例2
image-20200511160232884
image-20200511160158563
例3
image-20200511205203321
image-20200511205144609
例4
image-20200511211758884
image-20200511211738785

物理应用

质心问题

例1
image-20200504002911771
image-20200504002943464
image-20200504003010939
image-20200504003034119

引力问题

例1
image-20200504003745942

做功问题

反抗重力做功

例1
image-20200504082553773
image-20200504082612752
例2
image-20200511215504230
image-20200511215447367
例3
image-20200511215753755
image-20200511215735083
image-20200511215724062

克服阻力做功

假设匀速做功

例1
image-20200504085219629
image-20200504085242815

压力问题

例1
image-20200504084207767
例2
image-20200508230329445
image-20200508230345062