evaluate the following integral : integral from 0 to 4 of (2-e^(-3x))dx and solve the following c. simpson 1/3 with n=4 in matlab

To evaluate the integral ∫(2 - e^(-3x))dx from 0 to 4 in MATLAB, you can use the integral function. Here's how you can do it:

main.m
f = @(x) 2 - exp(-3*x);
result = integral(f, 0, 4);
disp(result);
66 chars
4 lines

This will give you the value of the integral.

Now, to solve the Simpson's 1/3 rule with n = 4 in MATLAB, you can use the integral function with the 'Method' option set to 'Simpson' and the 'Points' option set to 4. Here's the code:

main.m
f = @(x) 2 - exp(-3*x);
result = integral(f, 0, 4, 'Method', 'Simpson', 'Points', 4);
disp(result);
100 chars
4 lines

This will give you the approximate value of the integral using Simpson's 1/3 rule with n = 4. Note that the 'Points' option specifies the number of subintervals, so for n = 4, we use 4 subintervals.