定積分練習(xí)題1

作者:日期:定積分練習(xí)題一.選擇題、填空題1p+2p+3p++npnp+i1.將和式的極限lim-(p>0)np+inT8A.f^dx0x2.將和式lim(」++n*n+1n+23?下列等于1的積分是oA.f1xdx0B.f1xpdxoC.f1C1)pdx00x+亍)表示為定積分.2noo(B.f1(x+1)dx0D.f1)pdx0nC』ldx04.f1lx2一41dx=o021A?323c?T220B?丁35?曲線y=cosx,xe[0<2兀]與坐標(biāo)周圍成的面積oo(25oD,ToA.4B.25oC—*2oD.36.f1(ex+e-x)dx=ooo(01oA.e+—e7?若m=f1exdx,0oB?2e1D.e——en=Jedx，則m與n的大小關(guān)系是1xA.m>noB.m<noC.m=noD?無法確定89.由曲線y二X2-1和x軸圍成圖形的面積等于S?給出下列結(jié)果:②f1(1-x2)dx；③2f1(x2-1)dx:④2』-1①f1(x2-1)dx；-1則S等于()A?①③ooB.③④ooC.②③oD?②④10.y=fx(sint+costsint)dt，貝0y的最大值是(00(1-x2)dx.-i7C.-二oD.0211?若f(x)是一次函數(shù)，且f1f(x)dx=5,f1xf(x)dx=，那么J2』—dx的值是0061xA.1oB?215?設(shè)f(x)=<sinx兀/VxV兀3，則ff(x)cos2xdx=()其余0(A)2(A)20(B)300(C)40(D)1(D)(B)19.定積分J2Isinx(D)(B)19.定積分J2Isinx-cosxIdx等于((A)0)(B)(A)40(B)-3。(C)1(D)—lo44定積分J"Vsinx-sin3xdx等于0定積分Jcosx一cos3xdx等于()0(A)0(C)(C)綜合題：16T/、97(D)巨(1J1dx(2)J1ln(1(C)綜合題：16T/、97(D)巨(1J1dx(2)J1ln(1-x)dx0x2—x—2o(3)J2(x2—x2+xCOS5x)dx-2⑷Je張“exj(1-Inx)lnx(5)J20dx3(3+2x—x2)2(6)J:tan2x[sin22x+ln(x+<1+x2)]dx-K.-2(7)J21dx02+^4+x2(14)用定積分定義計算極限：im(nT8nnn、++...+)n2+1n2+22n2+n2定積分練習(xí)題2.J1(1+x)11—x2dx二()-17171⑷兀(B)0(C)2兀(D)-243.設(shè)feC[0,1]，且Jif(x)dx二2，則J2f(cos2x)sin2xdx=((C)邁+1(D)(C)邁+120.定積分J2max{x3,x2,1}dx等于()-2(B)(A)0(B))。4.設(shè)f(x)在［a,b］上連續(xù)，且fbf(x)dx二0，則()。a(A)在［a,b］的某個子區(qū)間上，f(x)=0；(B)在［a,b］上,f(x)三0；(C)在［a,b］內(nèi)至少有一點c,f(c)=0；(D)在［a,b］內(nèi)不一定有x，使f(x)=0。5.\；x3一2X2+xdx=()4L(A)15(2+\：2)4一15(2i2)dxdx=(1ex6..f1-一il+ex(A)-1(B)(C)占(D)1一e填空、選擇題(12sin(12sin8xdx二0ffi.,2cos7xdx二0ffxtsintdt(2)lim0—xTOln(1+x)⑶f2-1TOC\o"1-5"\h\z|x2-2x|dx二;曲線y二fxt(1一t)d的上凸區(qū)間是;f0J1+cos2xdx二;⑹設(shè)f(x)是連續(xù)函數(shù)，且f(x)二sinx+fKf(x)dx,貝U：f(x)二f1x(1+x2005)(ex一e-x)dx二;-11f1limJxln(1-)dt二;xT+gx1t定積分練習(xí)題一?計算下列定積分的值(1)J3(4x一x2)dx；(2)f2(x一1)5dx；-ii

(3)f2(x+sinx)dx；(4)f2cos2xdx；0一K2⑹嚴(yán)+3)dx;(7)JEdxfe2dx(8)exlnx；(9)J寧dx(IO)J3tan2xdx⑴）如xV）dx；（12）t啟；(13)J；|(lnx)2dxe(14)J2COS5xsin2xdx;(15)()oJ2exsinxdx;—，00(x2—x+l)3/2dxcosx齊.17)J2dx；17)01+sin2x(⑻；oex+e—x三.利用定積分求極限(1)limns11++?…+(n+1)2(n+2)2(n+n)2,、lim(2)nT8n(-+-+???+丄);n2+1(n2+2)2n2定積分練習(xí)題一、填空題：1.如果在區(qū)間［a,b］上，f(x)三1，則Jbf(x)dx二a2.J1(2x+3)dx二.0設(shè)f(x)=Jxsin12dt，則f'(x)=.0設(shè)f(x)=J1e-12dt，貝0f，(x)=.cosxJcos5xsinxdx二0J2sin2n—1xdx二,—2J+」dx=.1x38.比較大小，J3x2dx1J3x3dx.i9.由曲線y=sinx與x軸,在區(qū)間［0,兀］上所圍成的曲邊梯形的面積為10.二、曲線y二x2在區(qū)間［0,1］上的弧長為.選擇題：1.設(shè)函數(shù)f(x)僅在區(qū)間［0,4］上可積，貝泌有J3f(x)dx=［］02.2.D.J0A.J2f(x)dx+J3f(x)dx02C.J5f(x)dx+J3f(x)dx05設(shè)'Jxdx,I=J2x2dx，則]

B.J-1f(x)dx+J3f(x)dx0-110f(x)dx+J3f(x)dx103.4.5.A.B.11>(t-1)3(t-2)dt則?dxy=J0A.2B.-2C.0Jax(2-3x)dx=2,則a=[]0A.2B.-1C.0D?1D.設(shè)f(x)=X2(X>0)X(X<0)CJi<12則J1f(x)dx=[]-1DJ1<12A.2J0xdx-iC.J1x2dx+J0xdx0-1

B.2J1x2dx0D.J1xdx+J0x2dx0-1Jxsin12dt6.limfxT01A?2=[]x21B?3C.D?1TOC\o"1-5"\h\z7.F(x)=Je-tcostdt,則F(x)在［0,兀］上有()0⑷F(號)為極大值，F(xiàn)(0)為最小值F(與)為極大值，但無最小值(B)F(弓)為極小值，但無極大值F(弓)為最小值，F(xiàn)(0)為最大值9.設(shè)f(x)是區(qū)間L,b］上的連續(xù)函數(shù),且Jx2-2f(t)dt=x-輕，則f⑵=()111(A)2(B)-2(C)(D)-444.5.7.04.5.7.010.定積分Jiln(1+x)dx01+x2=((A)(B)(C)In2(D)兀2-ln2810.定積分Jiln(1+x)dx01+x2=((A)(B)(C)In2(D)兀2-ln2811.定積分tan2x,dxJ4嚴(yán)1+e-x4(A)(C)121兀1+2(D)1兀+—421-‘413.設(shè)函數(shù)feR[a,b],則極限limJf(x)nT+g0IsinnxIdx等于()(A)(B)(C)(D)不存在14.設(shè)f(x)為連續(xù)函數(shù)，且滿足Jxf(t-x)dt=-+e-x-1，則f(x)=(02o(A)-x-e-x(B)x+ex(C)—x+e-x(D)x-ex15.設(shè)正定函數(shù)feC[a,