微积分第三章习题参考答案(1).pptVIP免费

第三章一元函数积分学习题参考答案§3.1不定积分的概念及计算(51-52)30251..1.().2..3..4.ln||arctan.5.csccottan.216.(sin).7.2.28.cottan2csc22cot2.xxpfxdxecxxcxxxccxxcexcxxcxcxc一22222222352251..1.(25())33225.3(ln2ln3)12.tan.1cos2252..1.(sin)cos2cot112sincot2sin,sin1()2,()ln||.xxxxxxpdxdxxcdxxcxpfxxxxxxxfxxfxxxcx二三2233352.2.:(),1(),()ln||,(,3),1,ln||1.().(1)(0)0,()3,(),(3)27();(2)()360,245().pyfxfxfxxcxecyxsttssttsttssttt解设曲线方程为则曲线过点曲线方程为3.用表示秒后物体离开出发点的距离米由得秒2222222252.:,.221.:(),2()(),()(),1()()(),21,,.2xxxxxxxxxxxxxxxxxxxxeeeepshxchxeeeshxeshxchxeechxechxshxeeeshxechxeeeshxechxe公式四证明都是的原函数532421.,ln|ln|.122.ln|sin|sinsinsin.53ln|sincos|23..(sincos)224..5.2sin,3sec.4xenecxcxxxxxcxxcnIxxcnnxIxcxtxt一.§3.2不定积分的换元法(53-54)22332223222222222tansec53.6.sec(tan)11cossin.1.1.;42.94941294arcsin.234xdatatdtpIatataxtdttccaaaaxIecdxxdxIxxxxc二42246875922264275353.3.cos(1cos)cos(cos2coscos)cos211coscoscos.7594.(sec1)secsec(sec2secsec)sec121secsecsec.753pIxxdxxxxdxxxxcIxxdxxxxdxxxxc154.sinsin[cos()cos()]2p1coscos[cos()cos()]215.(cos2cos12)2Ixxdx11sin2sin12.424xxc222(3)1(22)26.2522525xdxxdxdxxxxxxx211ln(25)arctan.22xxxc222222222254..1.sin,sin1(1cos2)(sin2)222arcsin.22pxatxdxatdtaxaatdtttcaxxaxca三令2222254.2.(1)44111212arcsin.2241(2)2sec,1122412arccos.2dxdxpxxxxdcxxxxtdxdttcxxcx解法解法令65332323236654.3.1,6611116(1)12366ln(1)2131616ln(11).pxtdxttdtdttttxxttdttttttcxxxxc...