how to calculate the definite antiderivative of a function in matlab

To calculate the definite antiderivative of a function in MATLAB, we can use the "integral" function.

Here is an example code demonstrating how to calculate the definite antiderivative of the function f(x) = x^2 from x = 0 to x = 1:

main.m
syms x
f = x^2; % define the function
F = int(f); % calculate the antiderivative
result = F(1) - F(0); % calculate the definite integral
disp(result); % print the result
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In this code, we define the function using the "syms" command, which tells MATLAB that "x" is a symbolic variable. We then use the "int" function to calculate the antiderivative of "f", and the resulting symbolic expression is stored in the variable "F". Finally, we use "F" to calculate the definite integral using the formula F(b) - F(a), where "a" is the lower limit of integration (0 in this case) and "b" is the upper limit of integration (1 in this case). The result is stored in the variable "result" and printed to the console using the "disp" command.

Note that we used the "syms" command to define the function as a symbolic expression. This is necessary to use the "int" function. If you have a function that is defined as a MATLAB function file or an anonymous function, you can still use the "integral" function to calculate the definite integral. For example, suppose we have the MATLAB function file "myfun.m" that calculates the function f(x) = x^2. We can calculate the definite integral of this function from x = 0 to x = 1 using the following code:

main.m
result = integral(@myfun, 0, 1);
disp(result);
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Here, we use the "integral" function with the function handle "@myfun" (which tells MATLAB to use the "myfun" function) and the limits of integration (0 and 1). The result is stored in the variable "result" and printed to the console using the "disp" command.