# Integrating a constant?

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L'O.G. on 8 Aug 2023
Commented: Walter Roberson on 8 Aug 2023
This is more of a physics question than a Matlab question, but given an instantaneous velocity vx and a time increment dt, how do you numerically integrate to get a displacement? Analytically, this would usually be pretty straightforward since you'd have a function for the velocity, but given that vx is just a number, how do you do this?

Walter Roberson on 8 Aug 2023
format long g
constant = 1.23456;
constantFun = @(x) constant*ones(size(x));
attempt1 = integral(constantFun, 0, 10)
attempt1 =
12.3456
attempt2 = integral(@(x)constant, 0, 10, 'ArrayValued', true)
attempt2 =
12.3456
That is, the trick is that unless you use ArrayValued, integral() is going to pass in a vector of locations to integrate at, and you need to return a value for each of those locations. If you were to try integral(@(x)constant, 0, 10) then it would pass in a vector x but you would be only returning a scalar result no matter how big x was, and that would fail.
L'O.G. on 8 Aug 2023
Edited: L'O.G. on 8 Aug 2023
Thanks, so that's numerically integrating over a function that is constant over the entire interval. Is that correct? Also, like in my original post (I know this is a conceptual question), does it even make sense to numerically calculate a displacement from an instantaneous velocity where the latter is a particular number rather than a function? I am trying to understand this.
Walter Roberson on 8 Aug 2023
If what you have is a vector of times and a vector of corresponding vx, then you can use cumtrapz . That function would also be suitable if what you have is a constant time-step and a vector of vx over time.

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