#Basic Integration
#INPUT a,b,n
a=0
b=pi/2
n=100
#Define y=f(x)
function y=f(x)
y=sin(x);
end
#Calculate
d=(b-a)/n;
s=0;
for i=0:n-1
xi=a+d*i;
s=s+f(xi)*d;
end
#OUTPUT
Sum=s
|
# Trapezoidal formula
#INPUT a,b,n
a=0
b=pi/2
n=100
#Define y=f(x)
function y=f(x)
y=sin(x);
end
#Calculate
d=(b-a)/n;
s=d*(f(a)+f(b))/2;
for i=1:n-1
xi=a+d*i;
s=s+f(xi)*d;
end
#OUTPUT
Sum=s
|
# Simpson's formula
#INPUT a,b,n
a=0
b=pi/2
n=100
#Define y=f(x)
function y=f(x)
y=sin(x);
end
#Calculate
m=n/2;
d=(b-a)/n;
s=(f(a)+f(b))*d/3;
for i=0:m-1
xi=a+d*(2*i+1);
s=s+4*f(xi)*d/3;
end
for i=0:m-1
xi=a+d*(2*i);
s=s+2*f(xi)*d/3;
end
#OUTPUT
Sum=s
|