1、3.3定积分与微积分基本定理,第三章导数及其应用,基础知识自主学习,课时作业,题型分类深度剖析,内容索引,基础知识自主学习,1.定积分的定义给定一个在区间a,b上的函数yf(x):将a,b区间分成n份,分点为ax0x1x2xn11),则a的值是 A.2 B.3 C.4 D.6,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,a2ln a13ln 2,解得a2.,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,6.(2017湖南长沙模拟)设a cos xdx,b sin xdx,则下列关系式成立的是 A.ab B
2、.ab1C.a1,sin 11cos 1,即ab.故选A.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,7.定积分 |x1|dx等于 A.1 B.1 C.0 D.2,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,8.一辆汽车在高速公路上行驶,由于遇到紧急情况而刹车,以速度v(t)73t (t的单位:s,v的单位:m/s)行驶至停止,则在此期间汽车继续行驶的距离(单位:m)是 A.125ln 5 B.825ln C.425ln 5 D.450ln 2,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,1
3、3,14,15,16,282425ln 5425ln 5.,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,2, (sin xcos x)dx(sin xcos x),解析所求面积S cos xdxsin x,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,11.(2017济南模拟)设a0,若曲线y 与直线xa,y0所围成封闭图形的面积为a2,则a .,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,解析,解析封闭图形如图所示,,12.已知二次函数yf(x)的图像如图所示,则
4、它与x轴所围成的面积为 .,解析根据f(x)的图像可设f(x)a(x1)(x1)(a0).因为f(x)的图像过(0,1)点,所以a1,即a1.所以f(x)(x1)(x1)1x2.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,解析,技能提升练,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,解析由题意得,所求阴影部分的面积,故选A.,解析,答案,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,A.S1S2S3 B.S2S1S3C.S2S3S1 D.S3S2S1,1,2,3,4,5
5、,6,7,8,9,10,11,12,13,14,15,16,方法二S1,S2,S3分别表示曲线yx2,y ,yex与直线x1,x2及x轴围成的图形的面积,通过作图易知S2S1S3.,拓展冲刺练,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16.若函数f(x)在R上可导,f(x)x3x2f(1),则 f(x)dx .,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,4,解析因为f(x)x3x2f(1),所以f(x)3x22xf(1).所以f(1)32f(1),解得f(1)3.所以f(x)x33x2.,本课结束,