Question

用matlab求积分问题

要求e^(x^2)在0到1上的积分，用矩形公式求，n的取值是10到100的所有整数。我这么写为什么不对？
clc;
clear;
a = 0;
b = 1;
Lvalue = 0
for n = 10:1:100
for x = 0:(b-a)/n:1-(b-a)/n
Lvalue = Lvalue + exp(x^2)
Lvalue = (b-a)/n *Lvalue
end
end
Lvalue

Answer 1

用积分的定义式Σf(x)dx。
取N=100,则dx ＝ 1/N =0.01
clc;
clear;

N = 100;
dx = 1/N;
x = 0:dx:1;
fx = exp(x.^2);
y = sum(fx*dx)

y =
1.4813

若想用for循环则
clc;
clear;
Lvalue = 0;
N = 100;
dx = 1/N;
for x = 0:dx:1
fx = exp(x^2);
Lvalue = Lvalue + fx*dx;
end
Lvalue

结果为

Lvalue =
1.4813

当N=10000时
Lvalue =
1.4628