Solution:- I have given the required below:-
A) function I1 = TrapezoidalRule2D(a, b, c, d, m, n, func)
h = (b-a)/m;
k = (d-c)/n;
I11 =0;
I12 =0;
I13 =0;
I14 =0;
I15 =0;
for i = 1:m-1
xi = a + i*(h);
I11 = I11 + func(xi, c);
I22 = I22 + func(xi, d);
end
for j = 1:n-1
yj = c + j*(k);
I13 = I13 + func(a, yj);
I14 = I14 + func(b, yj);
end
for j = 1:n-1
for i = 1:m-1
xi = a + i*(h);
yj = c + j*(k);
I15 = I15 + func(xi, yj);
end
end
I1 = (h)*(k)*(0.25)*(func(a,c) + func(b,c) + func(a,d) + func(b,d)
+ 2*(I11 + I12 + I13 + I14) + 4*(I15));
end
B)
function I2 = SimpsonRule2D(a, b, c, d, m, n, func)
h = (b-a)/2*(m);
k = (d-c)/2*(n);
I21 =0;
I22 =0;
I23 =0;
I24 =0;
I25 =0;
I26 =0;
I27 =0;
I28 =0;
I29 =0;
I210 =0;
I211 =0;
I212 =0;
for j = 1:n
yj = c + (2*(j) - 1)*(k);
I21 = I21 + func(a, yj);
I23 = I23 + func(b, yj);
end
for j = 1:n-1
yj = c + 2*j*(k);
I22 = I22 + func(a, yj);
I24 = I24 + func(b, yj);
end
for i = 1:m
xi = a + (2*(i) - 1)*(h);
I25 = I25 + func(xi, c);
I26 = I26 + func(xi, d);
end
for i = 1:m-1
xi = a + 2*i*(h);
I27 = I27 + func(xi, c);
I28 = I28 + func(xi, d);
end
for j = 1:n
for i = 1:m
xi = a + (2*(i) - 1)*(h);
yj = c + (2*(j) - 1)*(k);
I29 = I29 + func(xi, yj);
end
end
for j = 1:n-1
for i = 1:m
xi = a + (2*(i) - 1)*(h);
yj = a + 2*(j)*(k);
I210 = I210 + func(xi, yj);
end
end
for j = 1:n
for i = 1:m-1
xi = a + 2*(i)*(h);
yj = c + (2*(j) - 1)*(k);
I211 = I211 + func(xi, yj);
end
end
for j = 1:n-1
for i = 1:m-1
xi = a + 2*(i)*(h);
yj = c + 2*(j)*(k);
I212 = I212 + func(xi, yj);
end
end
I2 = (1/9)*(h)*(k)*(func(a,c) + func(b,c) + func(a,d) + func(b,d) + 4*(I21 + I23 + I25 + I26 + I212) + 2*(I22 + I24 + I27 + I28) + 8*(I210 + I211) + 16*(I29));
end
I hope it solves your problem if you have any doubt please ask in the comments and if you liked the solution please upvote. Thanks.
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