不定积分习题库

不定积分习题库不定积分习题库不定积分习题库xxx公司不定积分习题库文件编号：文件日期：修订次数：第1.0次更改批准审核制定方案设计，管理制度MACROBUTTONMTEditEquationSection2SEQMTEqn\r\hSEQMTSec\r1\hSEQMTChap\r1\h第五章不定积分复习资料练习题学生学习档案要求：仔细，认真！一选择题:1.若SKIPIF1<0,则SKIPIF1<0().(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.2.如果SKIPIF1<0是SKIPIF1<0的一个原函数,SKIPIF1<0为不等于0且不等于1的其他任意常数,那么()也必是SKIPIF1<0的原函数。(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.3.下列哪一个不是SKIPIF1<0的原函数().(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.4.SKIPIF1<0().(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.5．设SKIPIF1<0，则SKIPIF1<0的一个原函数是（）(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.6．设SKIPIF1<0，则SKIPIF1<0为（）(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.7.SKIPIF1<0()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.8.SKIPIF1<0=()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.9.SKIPIF1<0()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.10.设SKIPIF1<0，则SKIPIF1<0（）(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.11.SKIPIF1<0()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.12.SKIPIF1<0()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.13.SKIPIF1<0()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.14.设SKIPIF1<0，则SKIPIF1<0（）(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.15.SKIPIF1<0()(a)SKIPIF1<0,(b)SKIPIF1<0,(c)SKIPIF1<0,(d)SKIPIF1<0.答案:........a....二填空题:1.设SKIPIF1<0,则SKIPIF1<0.2.经过点(1,2),且其切线的斜率为SKIPIF1<0的曲线方程为.3.已知SKIPIF1<0,且SKIPIF1<0时SKIPIF1<0,则SKIPIF1<0.4.SKIPIF1<0.5.SKIPIF1<0.6.SKIPIF1<0.7.SKIPIF1<0.8.SKIPIF1<0.9.SKIPIF1<0.10.SKIPIF1<0.11.SKIPIF1<0.12.SKIPIF1<0=.13.SKIPIF1<0.14.SKIPIF1<0.15.SKIPIF1<0.答案:SKIPIF1<011:SKIPIF1<0.12:SKIPIF1<0.13:SKIPIF1<0.14:SKIPIF1<0.15:SKIPIF1<0.三应用题:已知某产品产量的变化率是时间SKIPIF1<0的函数SKIPIF1<0(SKIPIF1<0是常数),设此产品SKIPIF1<0时的产量函数为SKIPIF1<0,已知SKIPIF1<0,求SKIPIF1<0已知动点在时刻SKIPIF1<0的速度为SKIPIF1<0,且SKIPIF1<0时SKIPIF1<0,求此动点的运动方程.已知质点在某时刻SKIPIF1<0的加速度为SKIPIF1<0,且当SKIPIF1<0时,速度SKIPIF1<0、距离SKIPIF1<0,求此质点的运动方程.设某产品的需求量SKIPIF1<0是价格SKIPIF1<0的函数,该商品的最大需求量为1000(即SKIPIF1<0时SKIPIF1<0),已知需求量的变化率(边际需求)为SKIPIF1<0,求需求量SKIPIF1<0与价格SKIPIF1<0的函数关系.设生产某产品SKIPIF1<0单位的总成本SKIPIF1<0是SKIPIF1<0的函数SKIPIF1<0,固定成本(即SKIPIF1<0)为20元,边际成本函数为SKIPIF1<0(元/单位),求总成本函数.设某工厂生产某产品的总成本SKIPIF1<0的变化率是产量SKIPIF1<0的函数SKIPIF1<0,已知固定成本为100元,求总成本与产量的函数关系.设某工厂生产某产品的边际成本SKIPIF1<0与产量SKIPIF1<0的函数关系为SKIPIF1<0,已知固定成本为1000,求成本与产量的函数.已知生产某商品SKIPIF1<0单位时,边际收益函数为SKIPIF1<0(元/单位),求生产SKIPIF1<0单位时总收益SKIPIF1<0以及平均单位收益SKIPIF1<0,并求生产这种产品1000单位时的总收益和平均单位收益.已知生产某商品SKIPIF1<0单位时,边际收益函数为SKIPIF1<0,求生产这种产品3000单位时的总收益和平均单位收益.设曲线通过点(1，2)，且其上任一点处的切线斜率等于这点横坐标的两倍，求此曲线的方程．答案:1:由题意得:SKIPIF1<0.又SKIPIF1<0,代入得SKIPIF1<0故SKIPIF1<0.2:由题意得:SKIPIF1<0,又SKIPIF1<0时SKIPIF1<0,代入得SKIPIF1<0,故SKIPIF1<0.3:由题意得:SKIPIF1<0,又当SKIPIF1<0时,速度SKIPIF1<0,代入得SKIPIF1<0,故SKIPIF1<0,从而有SKIPIF1<0,又SKIPIF1<0时SKIPIF1<0,故SKIPIF1<0.得SKIPIF1<0.4:由题意得:SKIPIF1<0SKIPIF1<0.又SKIPIF1<0时SKIPIF1<0,故SKIPIF1<0.5:由题意得:SKIPIF1<0.又固定成本(即SKIPIF1<0)为20元,代入得SKIPIF1<0.故SKIPIF1<06:SKIPIF1<0,又已知固定成本为100元,即SKIPIF1<0,代入得SKIPIF1<0,故SKIPIF1<0.SKIPIF1<07:SKIPIF1<0,又已知固定成本为1000元,即SKIPIF1<0,代入得SKIPIF1<0,故SKIPIF1<0SKIPIF1<0.8:SKIPIF1<0,又SKIPIF1<0,故SKIPIF1<0,得SKIPIF1<0,SKIPIF1<0.SKIPIF1<0(元).SKIPIF1<0(元).9:SKIPIF1<0,又SKIPIF1<0,故SKIPIF1<0,得SKIPIF1<0,SKIPIF1<0.SKIPIF1<0.10:设所求的曲线方程为yf(x)，按题设，曲线上任一点(x,y)处的切线斜率为SKIPIF1<0＝２x，即f(x)是2x的一个原函数．因为SKIPIF1<0dxSKIPIF1<0＋C，故必有某个常数C使f(x)SKIPIF1<0＋C，即曲线方程为ySKIPIF1<0＋C．因所求曲线通过点(1，2)，故21+C,C1．于是所求曲线方程为ySKIPIF1<0＋１．四计算题：1SKIPIF1<0dx2SKIPIF1<0dx3、SKIPIF1<0dx4SKIPIF1<0dx5SKIPIF1<0dx6SKIPIF1<0dx7SKIPIF1<0dx8SKIPIF1<0dx9SKIPIF1<0dx10SKIPIF1<011SKIPIF1<0SKIPIF1<0dx12SKIPIF1<0xdx13SKIPIF1<0dx14SKIPIF1<015SKIPIF1<0dx16SKIPIF1<017SKIPIF1<018SKIPIF1<019SKIPIF1<020SKIPIF1<021SKIPIF1<022SKIPIF1<023SKIPIF1<024SKIPIF1<025SKIPIF1<026SKIPIF1<027SKIPIF1<028SKIPIF1<029SKIPIF1<030SKIPIF1<0解答：原式=SKIPIF1<0dx+SKIPIF1<0dxSKIPIF1<0dx+3SKIPIF1<0dxSKIPIF1<0＋lnSKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0+C．2、原式=SKIPIF1<0dxSKIPIF1<0dxSKIPIF1<0－x+arctanx+C．3、原式=SKIPIF1<0dxSKIPIF1<0dxSKIPIF1<0tanxx+C．4、原式=SKIPIF1<0（１cosx)dxSKIPIF1<0∫(1cosx)dxSKIPIF1<0(xsinx)+C．5、原式=SKIPIF1<0。6、原式=SKIPIF1<0。7、原式=SKIPIF1<0。8、原式=SKIPIF1<0。9、原式=SKIPIF1<0·２dxSKIPIF1<0·（２x)′dx＝SKIPIF1<0udu＝sinu+C．再以u2x代入，即得SKIPIF1<0cos2xdxsin2x+C.10、原式=SKIPIF1<0dxSKIPIF1<0·SKIPIF1<0(2x+5)dx＝SKIPIF1<0SKIPIF1<0d(2x+5)＝SKIPIF1<0SKIPIF1<0duSKIPIF1<0lnSKIPIF1<0+C＝SKIPIF1<0lnSKIPIF1<0+C．11、原式=SKIPIF1<0SKIPIF1<0dx＝SKIPIF1<0SKIPIF1<0d(1SKIPIF1<0）SKIPIF1<0SKIPIF1<0SKIPIF1<0duSKIPIF1<0+CSKIPIF1<0SKIPIF1<0+C．12、原式=SKIPIF1<0sinxdxSKIPIF1<