How does one use integral2 (double integral) symbolically?

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.

[Dipak kumar Panigrahy]

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?

Answer 1

[Shashank Prasanna]

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

[Mikayel]

Dear Shashank, thank you for the response. I have the Symbolic Toolbox installed, what I didn't find in the help is, how to calculate the double integral.

Could you please help with the specific command that I should input to get (1-exp(-y))*(1-exp(-x)) from the double integration of cdf=@(u,v) exp(-(u+v)).

[Shashank Prasanna]

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

[Mikayel]

Thank you so much!

Answer 2

[Okae]

how do i type j=\iint\of V_s\ [f\left(\varepsilon_{\left(\left(p+q\right)\right)}-f\left(\varepsilon_p\right)\delta\left(\varepsilon_{\left(\left(p+q\right)\right)}-\varepsilon_p-\hbar\omega q\right)\right]dp_{\left(x\right)d}p_y

in symbolic math toolbox?