定积分重积分及其应用答案

1、定积分、重积分及其应用、基本题x22f 兀 r1、设 F(x)= Ltcos2tdt= F(x) = xcos2x= F 才兀2兀=cos 442、设半(X )= f Jdt + f e土dt= A(x) = e(x j fx2)e，=2xex3、设 f(x)=i：Wdt= f(xZ+Qx)2 =3J1+ 9x2 -3e3xj1 +ex3x 3x2d x2x2d x2x2d x t2x24、 一 fe dx =e ; J一e dx =e +c ； 一 J e dt =e ；dx、dxdx 1兀95、j x cosxdx =0 ；f(X3 +1 “1 -X2dx = 1 X3 J1 -x2dx

2、+ f J1 -x2dx = 0 + 巴=S*-J2&下列式子中正确的是fdx 132ex dx = 0(a 狀 f (x)dx f|f (xjdxb(b) f(x)dx(cU f (xjdx = alfjclx（d ）无法确定7、设 h 二xdx, J 揺tanxdx, fsinxdx,(a)liAl2Al3(b)l2Alil3(cHsAJaIi(d)l2Al3li设 f（X 在 a,b 】上满足，f （X ）cO, f （X ）:0。b1令 l1 = f(x)dx , l2=f(bXb-a), l3=2Lf(a)+f (b)(b-a),则(B )(a)I1VI2I3(bjjvhvj (c)

3、l3N1l2(djjwjvh9、2x0 W(e2-1);；0(3210 d3L(3211 I / -11oil k .F5 一2);-1f4 sin 2xdx =cos2x(4 =P2010、+1 )；11、12、13、1 1 1 1 ,dx= r (2x2 +1 pd(2x2 +1 X-j2x2+14COMdx=2sin7x1 vxdx.3 sin YdxXI 3 eln X ,dx Xe21e xln2x141 =2(si n2 -s in1)|fegd(37X+1)3弄十9104八 1 =e -e1 ? . 3,33sin -d- =cos-3 1 X X12=4os31 2e 3 1=

4、f ln xd ln X =ln14e2_2dx =In xdln X =-JeIn xe2eX_1 12 .14、设f XX =2，贝U ( f (x-1 )dx = J f (t )d(t 卅IrI冗 J f(t)(t1 )dtJ f(t)d2=15、判定下列广义积分的敛散性:切n XeX-be dx = fe1dx =x(ln x )P = -1 1，发散e xlnxdx=P =1 ,发散;-be 1dx =e X Jln X1pS1，收敛;1I-xw =e lim e =e，x-尹-x11f 一 dx= p =1,发散;1 x-bef Txdx =11p =-丄，发散2收敛;)=处，发

5、散乂 1-)dx-oG2+x2七c1X 1X2 d = = arctanX、忑近421 +1 =丿-F-72(2 I 2 丿丿 2JI-be 1-be,2dxy X2 +2x+62dxx(x+1 )+(75)d11丄 x+1arcta n75-heV5JI5则 JJ3db =3兀(41) = 9兀D16、设 D =(x, y * x2 +y2 4，17、设 D = (X, y jx2 + y2如，则JJ J9”*挣=6兀二重积分的几何意义118、平面区域D由x=0,y=0,x + y = -，x + y =1所围成,l1,lJJIn(X +y )dcr ,2 I的大小关系是I2川x + y )

6、dcr ,I3JJsi n x+yd，则T3T119、交换下列积分次序:1 x1)；dx2f(x,y)dy1jydyjy f(x,y)dx2 2y4 护2).0 dy 卜 f (x, y )dx = J。dx f (x, y )dy21J1 =222兀020、二次积分 Jjdx.0f(X + y )dy = J0 d日 J0 f (r21、设O 为 X2 +y2 +z2 0 )则 H2dv = 2 川dv = 2-兀(3 , = 36兀QQ2 3二、计算题1、Ixmox t20esint dtxtan2 Xx2 sin(ex -1) lim01f tl ntdtPosx2、J2兀sin4 x(sin x + cosx )dx ；2xe .77 dx ；1 +ee2 1 + lnx丽dx3、.4 1仮(1 +x)dx;Jdx X4、5、cosxdx ；27、设X 1 dx ;L xln(x+ 1)dx；J： Jx2 -4x +4dx ;兀0 xcosxdx ;fe%xfjsinx-