How does one use integral2 (double integral) symbolically?

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Mikayel
Mikayel 2013-8-22
评论： Dipak kumar Panigrahy 2020-5-21
I would like to get some help on how to use the integral2 symbolically?
E.g. I have a Joint PDF function -> "@(x,y) exp(-(x+y))"
To verify that it adds up to one, I did the following -> "integral2(pdf,0,inf,0,inf)" with the result being 1 as expected.
Now to calculate the Joint CDF symbolically I defined x and y as symbols and tried to do -> "cdf=@(u,v) exp(-(u+v))" and "integral2(cdf,0,x,0,y)". The error I got was -> "Error using integral2. XMAX must be a floating point scalar."
What I want to get is -> "(1-exp(-y))*(1-exp(-x))" !!
Your help will be much appreciated.
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Dipak kumar Panigrahy
Dipak kumar Panigrahy 2020-5-21
clear
clc
syms rtstar
syms rt1 v delta R do %or assign numeric values to the variables
p=10;
cdf1=p*tan(delta)*R^2;
cdf2=p*tan(delta)*R^2;
eqn = ss == (int(int(cdf1,rt,rt1,rtstar),e,0,v)-int(int(cdf2,rt,rtstar,rt2),e,0,v));
sol = solve(eqn, rtstar)
can ayone tell me how to solve this eqn?

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Shashank Prasanna
Shashank Prasanna 2013-8-22
From the documentation of integral2:
integral2
Numerically evaluate double integral
http://www.mathworks.com/help/matlab/ref/integral2.html
It is not meant for symbolic computation. If you are interested in symbolic results you need to have Symbolic Toolbox installed
Then you can use the int function:
http://www.mathworks.com/help/symbolic/int.html
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Shashank Prasanna
Shashank Prasanna 2013-8-23
编辑：Shashank Prasanna 2013-8-23
Sir, you have to use functions from the Symbolic Toolbox.
>> syms u v
>> cdf = exp(-(u+v))
>> int(int(cdf,v,0,v),u,0,u)
http://www.mathworks.com/help/symbolic/int.html

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