How to integrate a function w.r.t. a variable that is not the input variable to the function

Question

liz 2016-9-8

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回答： Michael Wang 2016-9-14

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Hi,

I have 2567x1 double variable which is a Strain, with a corresponding time variable.

I have a function:

function [y]=mystrainrate(reflectedstrain)
   c=4980;
   l_s=6*10^-3;
   y=c*(reflectedstrain)/l_s;
end

I want the integral of y with respect to time between 0 and a specified time. But I want to plot it, so essentially I want a loop to find the integral up to each time index from 1 to 2567 and create another 2567x1 variable of the integrals.

But, I can't work out how to integrate a function with respect to a variable that is not the input variable to the function.

For example, I currently have this code:

for i=1:length(reflectedstrain)
  nominalstrain(i,1)=integral(@mystrainrate,0,time(i));
end

But obviously this integrates the strain rate function w.r.t. the strain and not w.r.t the time.

Any help would be appreciated. Thanks.

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Answer 1

Michael Wang 2016-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/302373-how-to-integrate-a-function-w-r-t-a-variable-that-is-not-the-input-variable-to-the-function#answer_234729

As you have mentioned, the function you are using as the input of the ‘integral’ function should be a function that w.r.t time ( i.e. y(t) or in other form y(reflectedstrain(t)) ).

The ‘ integral ’ function in this case will not work due to the relation between "reflectedstrain" and time "t" are not constant so the input function varies from time to time. I would recommend you to calculate the integral value numerically (e.g. integral_y = y (i)*delta_t ) assuming you can calculate the time difference "delta_t" between time steps.

You could also try to integrate the “y” value using ‘ trapz ’ function.

Hope these help!