实验五数值积分参考答案.docVIP

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?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。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 ,, ? 7.1 syms x; g1=int(x.*sin(x).*sin(x)) g1 = x*(-1/2*cos(x)*sin(x)+1/2*x)+1/4*sin(x)^2-1/4*x^2 clear;syms x; d1=diff(x*(-1/2*cos(x)*sin(x)+1/2*x)+1/4*sin(x)^2-1/4*x^2) syms x; g2=int(1/(1+cos(x))) g2 = tan(1/2*x) clear;syms x; d2=diff(tan(1/2*x)) syms x; g3=int(1/(exp(x)+1)) g3 = log(exp(x))-log(exp(x)+1) clear;syms x; d3=diff(exp(x))-log(exp(x)+1)) syms x; g4=int(finverse(sin(x))) g4 = x*asin(x)+(1-x^2)^(1/2) clear;syms x; d4=diff(x*asin(x)+(1-x^2)^(1/2)) syms x; g5=int(sec(x).^3) g5 = 1/2/cos(x)^2*sin(x)+1/2*log(sec(x)+tan(x)) clear;syms x; d5=diff(1/2/cos(x)^2*sin(x)+1/2*log(sec(x)+tan(x))) 7.2 x=10e-100:0.001:1; y=sin(x)./x; trapz(x,y) clear all;syms x; int(sin(x)/x,x,0,1) x=0:0.001:1; y=x.^x; trapz(x,y) clear all;syms x;syms esp; x1=log(esp);x2=log(1); int(exp(x),x,x1,x2) 注释：根据公式 x.^x=exp(x*log(x)) clear all;syms x; 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) clear all;syms x; int(exp(x)*sin(2*x),x,0,2*pi) x=0:0.001:1; y=exp(-x.*x); trapz(x,y) clear all;syms x; int(exp(-x*x),x,0,1) 7.3 syms x; int((4*sqrt((36-4*x*x)/9)),x,0,3) 7.4 clear;syms x y; int(int(1+x+y,y,1-sqrt(1-x.^2),1+sqrt(1-x.^2)),x,-1,1) 7.5 int(exp(-x*x)/(1+x*x*x*x),x,-inf,inf) int(tan(x)/sqrt(x),x,0,1) int(sin(x)/sqrt(1-x*x),x,0,1)