matlab积分函数.doc

matlab积分函数一.相关函数: %符号积分int(f,v)int(f,v,a,b)%数值积分trapz(x,y)%梯形法沿列方向求函数Y关于自变量X的积分cumtrapz(x,y)%梯形法沿列方向求函数Y关于自变量X的累计积分quad(fun,a,b,tol)%采用递推自适应Simpson法计算积分quad1(fun,a,b,tol)%采用递推自适应Lobatto法求数值积分dbquad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol)%二重(闭型)数值积分指令triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol)%三重(闭型)数值积分指令二.示例:例1:计算f(t)=exp(-t2)在0,1上的定积分本例演示:计算定积分常用方法symsxint(exp(-x2),0,1)ans=1/2*erf(1)*pi(1/2)%erf为误差函数vpa(int(exp(-x2),0,1)ans=.7468241328124270d=0.001;x=0:d:1;d*trapz(exp(-x.2)ans=0.7468quad(exp(-x.2),0,1,1e-8)ans=0.7468例2:计算f(t)=1/log(t)在0,x,0x1-处为负无穷本例演示:用特殊函数表示的积分结果,如何用mfun指令（1）symstxft=1/log(t);sx=int(ft,t,0,x)sx=-Ei(1,-log(x)%完全椭圆函数（2）x=0.5:0.1:0.9sx_n=-mfun(Ei,1,-log(x)x=0.50000.60000.70000.80000.9000sx_n=-0.3787-0.5469-0.7809-1.1340-1.7758（3）%图示被函数和积分函数clfezplot(1/log(t),0.1,0.9)gridonholdonplot(x,sx_n,LineWidth,3)Char1=1/ln(t);Char2=int_0x1/ln(t)dt;title(Char1,and,Char2)legend(Char1,Char2,Location,SouthWest)例3:计算f(t)=exp(-sin(t)在0,4上的定积分注意:本题被函数之原函数无封闭解析表达式,符号计算无法解题!本例演示:符号计算有限性（1）符号计算解法symstxft=exp(-sin(t)sx=int(ft,t,0,4)ft=exp(-sin(t)Warning:Explicitintegralcouldnotbefound.Iat58sx=int(exp(-sin(t),t=0.4)（2）数值计算解法dt=0.05;%采样间隔t=0:dt:4;%数值计算适合于有限区间上,取有限个采样点Ft=exp(-sin(t);Sx=dt*cumtrapz(Ft);%计算区间内曲线下图形面积,为小矩形面积累加得Sx(end)%所求定积分值%图示plot(t,Ft,*r,MarkerSize,4)holdonplot(t,Sx,.k,MarkerSize,15)holdoffxlabel(x)legend(Ft,Sx)ans=3.0632例4:绘制积分图形,y=2/3*exp(-t/2)*cos(sqrt(3)/2*t);积分s(x)=int(y,t,0,x)于0,4*pi上symsttaoy=2/3*exp(-t/2)*cos(sqrt(3)/2*t);s=subs(int(y,t,0,tao),tao,t);%获得积分函数subplot(2,1,1)%ezplot(y,0,4*pi),ylim(-0.2,0.7)