find displacement using calculus in matlab

To find displacement using calculus in Matlab, we need to integrate the velocity function to derive the position function. We can use the integral function in Matlab to perform numerical integration. Here's an example:

main.m
% define the velocity function
v = @(t) 3*t^2 + 2*t + 1;

% set the initial position and time
x0 = 0;
t0 = 0;

% define the integral function using anonymous function
x = @(t) integral(v, t0, t) + x0;

% find the displacement at time t = 2
disp = x(2);
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In this example, we first define the velocity function v as an anonymous function. Then, we set the initial position x0 and time t0. Next, we define the position function x as an anonymous function using integral function to integrate v with respect to t from t0 to t. Finally, we find the displacement at time t = 2 using the position function x.

Note that we can use numerical differentiation function diff to derive the velocity function v from the position function x, if the latter is given as a discrete data set.