07-定积分的近似计算课件

定积分的近似计算矩形法nba0i1f(x)dxlimf(i)xi．函数f(x)在[a,b]上的定积分nbiani1f(x)dxlim函数f(x)在[a,b]上连续时，对[a,b]进行n等分inxbanini1babanf()f()．12nnba(yyy)．0nbbaf(x)dx(yay1yn1)nnbnnanbabaf(x)dxlimf(i)i1f(i)．i1函数f(x)在[a,b]上连续时，对[a,b]进行n等分记yif(xi)，则ii1xixiabxyOyf(x)定积分baf(x)dx(f(x)0)的几何意义baf(x)dxA．AabxyOyf(x)0nbbaf(x)dx(yay1yn1)12nnba(yyy)．左矩形法右矩形法矩形法iii101x2解记xi，y4(i0,1,2,,10)，12041xdx．例利用矩形法(n10)计算xi00.10.20.30.40.50.60.70.80.91.0yi4.00003.96043.84623.66973.44833.22.94122.68462.43902.20992.00001020410dx1(yy1y9)3.2400，11210201x4101xdx1(yyy)3.0400．梯形法abxyOyf(x)01nn1bbaf(x)dx(yayy)12nnba(yyy)．abxyOyf(x)022bnann1yybaf(x)dxyy1y1y2梯形法0122n2bayynyyn1y．解12041xdx．例利用梯形法(n10)计算xi00.10.20.30.40.50.60.70.80.91.0yi4.00003.96043.84623.66973.44833.22.94122.68462.43902.20992.0000122014dx1y0y10yy91x102y3.1400．iii101x2记xi，y4(i0,1,2,,10)，抛物线法（辛普森法）abxyOyf(x)01nn1bbaf(x)dx(yayy)12nnba(yyy)．左矩形法yyi1右矩形法yyiabxyOyf(x)0122banyynbaf(x)dxyyn1y．梯形法ii1yi1yyi(xxi1)yi1xx043nn2bbaf(x)dx[(yyn)2(y2yay)抛物线法iypx2qixri其中n为偶数．4(y1y3yn1)]．辛普森法解12041xdx．例利用抛物线法(n10)计算xi00.10.20.30.40.50.60.70.80.91.0yi4.00003.96043.84623.66973.44833.22.94122.68462.43902.20992.0000120430dx1[(yy)2(yyyy)01024681x3.1416．4(y1y3y5y7y9)]iii101x2记xi，y4(i0,1,2,,10)，1204dx3.24001201x4dx3.0400左矩形法右矩形法梯形法1201x4dx3.14001201x4dx3.1416抛物线法1201x41xdx3.14159265小结1.矩形法；2.梯形法；3.抛物线法(辛普森法)．