Numerical integration in MATLAB

Hello everyone,

I am trying to first numerically integrate a function and then plot the output of the integral. However, I have a variable T which is in the range (1:1000). I am not sure how to use a loop in integral and then plot values for all T with the corresponding value of integral. The MATLAB code is:

Hello everyone,

I am trying to first numerically integrate a function and then plot the output of the integral. However, I have a variable T in the integral which is in the range (1:1000). I am not sure how to use a loop in integral and then plot values for all T with the corresponding value of integral. The MATLAB code is:

kb = 1.38 .* 10.^-23;
h = 1.05 .* 10.^-34;
wd = 6.94 .* 10.^13;
vs = 6084;
B1 = 2.7 .* 10.^-19;
B2 = 170;
A1 = 2 .* 10.^-45;
D = 0.004;
T = 300;
c = (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);

T = 1:1000;

fun = @(x) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2/T)) + (D.*A1 .* x.^4) + vs)));
K = c .* integral(fun,0,wd)

plot(T, K)

Thanks in advance,

Raj Patel.

[Raj Patel]

The code is:

(Note: I removed a line where T was defined 2nd time)

Thanks in advance,

Raj Patel.

kb = 1.38 .* 10.^-23;
h = 1.05 .* 10.^-34;
wd = 6.94 .* 10.^13;
vs = 6084;
B1 = 2.7 .* 10.^-19;
B2 = 170;
A1 = 2 .* 10.^-45;
D = 0.004;
c = (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);

T = 1:1000;

fun = @(x) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2/T)) + (D.*A1 .* x.^4) + vs)));
K = c .* integral(fun,0,wd)

plot(T, K)

Answer 1

[Star Strider]

Try this:

c = @(T) (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);
fun = @(x,T) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2/T)) + (D.*A1 .* x.^4) + vs)));

T = 1:1000;for k = 1:numel(T)
    K(k) = c(T(k)) .* integral(@(x)fun(x,T(k)),0,wd);
end

figure
plot(T, K)
grid
xlabel('T')
ylabel('K')

producing:

Since both ‘c’ and ‘fun’ are functions of ‘T’, they need to be coded as such.

[Raj Patel]

Thanks Star.

[Star Strider]

As always, my pleasure!

It can be fully vectorised, avoiding the loop, using the 'ArrayValued' name-value pair:

c = @(T) (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);
fun = @(x,T) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2./T)) + (D.*A1 .* x.^4) + vs)));

T = 1:1000;
K = c(T) .* integral(@(x)fun(x,T),0,wd,'ArrayValued',1);

figure
plot(T, K)
grid
xlabel('T')
ylabel('K')

producing the same plot. The ‘fun’ code changed slightly to make it fully vectorised.

[Raj Patel]

Oh! I see.

Thanks,

Raj Patel.

[Star Strider]

As always, my pleasure!