资源描述:
《实验五 数值积分参考答案》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、一实验目的: 1 加深理解积分理论中分割、近似、求和、取极限的思想方法;2 了解定积分近似计算的矩形法、梯形法与抛物线法;3 会用MATLAB语言编写求定积分近似值的程序,会用MALAB中的命令求定积分。二实验准备素材见附件。三实验内容1.(不定积分)用int计算下列不定积分,并用diff验证,,,,2.(定积分)用trapz,int计算下列定积分,,,3.(椭圆的周长)用定积分的方法计算椭圆的周长4.(二重积分)计算积分5.(广义积分)计算广义积分,, 7.1symsx;g1=int(x.*sin(x).*sin(x))g1=x*(-1/2*cos(x
2、)*sin(x)+1/2*x)+1/4*sin(x)^2-1/4*x^2clear;symsx;d1=diff(x*(-1/2*cos(x)*sin(x)+1/2*x)+1/4*sin(x)^2-1/4*x^2)symsx;g2=int(1/(1+cos(x)))g2=tan(1/2*x)clear;symsx;d2=diff(tan(1/2*x))symsx;g3=int(1/(exp(x)+1))g3=log(exp(x))-log(exp(x)+1)clear;symsx;d3=diff(exp(x))-log(exp(x)+1))symsx;g4
3、=int(finverse(sin(x)))g4=x*asin(x)+(1-x^2)^(1/2)clear;symsx;d4=diff(x*asin(x)+(1-x^2)^(1/2))symsx;g5=int(sec(x).^3)g5=1/2/cos(x)^2*sin(x)+1/2*log(sec(x)+tan(x))clear;symsx;d5=diff(1/2/cos(x)^2*sin(x)+1/2*log(sec(x)+tan(x)))7.2x=10e-100:0.001:1;y=sin(x)./x;trapz(x,y)clearall;symsx
4、;int('sin(x)/x',x,0,1)x=0:0.001:1;y=x.^x;trapz(x,y)clearall;symsx;symsesp;x1=log(esp);x2=log(1);int('exp(x)',x,x1,x2)注释:根据公式x.^x=exp(x*log(x))clearall;symsx;x1=log(10e-100);x2=log(1);int('exp(x)',x,x1,x2)x=0:0.001:2*pi;y=exp(x).*sin(2*x);trapz(x,y)clearall;symsx;int('exp(x)*sin(2
5、*x)',x,0,2*pi)x=0:0.001:1;y=exp(-x.*x);trapz(x,y)clearall;symsx;int('exp(-x*x)',x,0,1)7.3symsx;int('(4*sqrt((36-4*x*x)/9))',x,0,3)7.4clear;symsxy;>>int(int(1+x+y,y,1-sqrt(1-x.^2),1+sqrt(1-x.^2)),x,-1,1)7.5int('exp(-x*x)/(1+x*x*x*x)','x',-inf,inf)int('tan(x)/sqrt(x)','x',0,1)int('
6、sin(x)/sqrt(1-x*x)','x',0,1)