plot integral

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mouna
mouna 2011-5-19
评论： Vignesh Sella 2020-2-28
good morning
I have this equationy(t)=integral of((C(t)*dt)) (0-->t) i haven't the equation of C(t) but i have the values of C(t) in each minute i need to plot y(t) how i can do it???
thanks in advance
  2 个评论
Yoav Livneh
Yoav Livneh 2011-5-19
How is y a function of t if you integrate C(t) over t?
Vignesh Sella
Vignesh Sella 2020-2-28
good morning!

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回答（2 个）

Sarah Wait Zaranek
Sarah Wait Zaranek 2011-5-26
This can be done using cumtrapz --
Doc here:
http://www.mathworks.com/help/releases/R2011a/techdoc/ref/cumtrapz.html
Code example below using points taken from a sine wave:
X = linspace(0,2*pi,100);
Y = sin(X);
Z = cumtrapz(X,Y);
plot(X , [Y; Z])
Charles Cunningham
Sarah, thank you for pointing out the use of cumtrapz. That answer also helped me make progress with a scrpit I'm wokring on. I did notice a discrepancy with the result for Z and it took a little bit to figure out why. So I thought I'd share what I found.
The integral of sin(x)dx is -cos(x).
After executing your code I expected to see the plot of Z to match a plot of -cos(x). However, it did not. To illustrate this point plot the following (based on Sarah's code):
plot(X , [Z; -cos(X)])
Notice that the result Z is -cos(x) offset by a constant.
I was then reminded of 2 things:
  1. The integral of f(x)dx is f(x)/dx + constant.
  2. That cumtrapz is an esimation to find an integral.
The estimation includes the constant. So you can correct the estimation of this integral by subtracting that constant. Then the proper result will be plotted. Update Z to the following equation:
Z = cumtrapz(X,Y) - 1;

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