定积分知识点汇总.docx

一定积分的几何意义定积分f(x)0时，Jbf(x)dx=Sf(x)0时，Jbf(x)dx=Sf(x)有正有负时,aaa二.定积分基本性质当a二b时，Jbf(x)dx=0.Jbkf(x)dx=kJbf(x)dxaJbf(x)dx=S,Jcf(x)dx=S,Jdf(x)dx=a1b一Jdf(x)dx=Jbf(x)dx+Jcf(x)dx+Jdf(x)dx面积和S+S+S=Jbf(x)dxJcf(x)dx+Jd3Jbf(x)g(x)dx二SJbf(x)土f(x)土土f(x)dx=Jbf(x)dxJbf(x)dxiJbf(x)dx2-a1Jbf(x)dx二Jcif(x)dx+Jc2f(x)dx+Jbf(x)dxc1若奇函数y=f(x)在a,a上连续不断，则Jaf(x)dx二0若偶函数y=f(x)在a,a上连续不断，则Jaf(x)dx二2Jaf(x)dx0S3二SS+S.123f(x)dx