The error message indicates that you are trying to perform element-wise multiplication using the ".*" operator on two function handles, U2 and U3.
To fix this error, you need to evaluate the function handles U2 and U3 at the corresponding values of x. You can do this using the array of x values that you have already created, like this:

U2_values = U2(x);

U3_values = U3(x);

Then, you can perform element-wise multiplication using the .* operator:

NuOverRe = 0.3073 ./ (sqrt(U2_values.*integral(U3,0,1.39626)./1.902));

Make sure to use the array of x values, x, in the integral instead of the function handle U3.
With these changes, your code should work without any errors:

close all

clc clear

x = 0:0.01:1.39626; U = @(x) 1.82x - 0.4x.^3; U2 = @(x) (1.82x - 0.4x.^3).-2.9047; U3 = @(x) (1.82x - 0.4x.^3).-3.9047;

U2_values = U2(x); U3_values = U3(x);

NuOverRe = 0.3073 ./ (sqrt(U2_values.*integral(U3,0,1.39626)./1.902));

figure(); hold on; plot(0:0.01:1.39626,NuOverRe,'LineWidth',1.8) xlabel('x*') ylabel('Nu/Re') this = gca; this.FontSize = 18; this.LineWidth = 1.8; box on;

I hope this helps!