Can anybody help me to solve this?

How can I compute this integral (numerical integration) in matlab?

integral (integral(f1(x))*integral(f2(x)))

where the inner integrals have same limit and the outer integral is from zero to infinity.

[madhan ravi]

@ASWATHI V it depends what f1 and f2 are so when you ask a question provide all the details if you want to get a perfect solution.

[ASWATHI V]

f1 =  @(y,x) exp(-(((x.*sig_2.*lamda_1)+(lamda_I1.*I.*alpha_1))./(I.*alpha_1)).*y);
f2 =  @(y,x) y+((lamda_I3.*I.*alpha_1)./(lamda_1.*x.*p_p));
f3 = @(y) integral(f1,(I/p_umax),inf);
f4 = @(y)  integral2(f2,(I/p_umax),inf);
f5 = @(y) f3(y).*f4(y);
f5 = integral(f5,0,inf);

This is what I required. integral (integral(f1(x,y)).*integral(f2(x,y)))

[madhan ravi]

what are the values of the variables other than x and y??

[ASWATHI V]

they are constants

[ASWATHI V]

They are constants

[madhan ravi]

upload the full code that you are trying , turns out all the questions you have asked so far is totally vague

[ASWATHI V]

int( int(f1(x), x, inner_limit_low, inner_limit_high) * int(f2(x), x, inner_limit_low, inner_limit_high), variable_of_outer_integration, 0, inf)

This is the thing i want. But when I am doing this and trying to plot this, it shows an error Can't plot this. It shows some error ''Error using plot

A numeric or double convertible argument is expected''

[Walter Roberson]

Is I the same as sqrt(-1) in your expressions?

[Walter Roberson]

f3 = @(y) integral(f1,(I/p_umax),inf);
f4 = @(y)  integral2(f2,(I/p_umax),inf);

You used integral2() for f2, but you only supplied one set of bounds. It should probably be integral()

[ASWATHI V]

''I'' is a constant.

I have changed integra2

Answer 1

[Walter Roberson]

After having defined f1 and f2 as symbolic functions, and assigning values to the limits

int( int(f1(x), x, inner_limit_low, inner_limit_high) * int(f2(x), x, inner_limit_low, inner_limit_high), variable_of_outer_integration, 0, inf)

Note that variable_of_outer_integration cannot be x: you defined the inner integrations as being definite integrals, so the function argument x will not appear in the result of their int()

[ASWATHI V]

Actually f1 and f2 are functions of x and y. So i have to do y first and then x. syms is not working here

[ASWATHI V]

Can't plot this. It shows some error ''Error using plot

A numeric or double convertible argument is expected''

[Walter Roberson]

syms x y
result = int( int(f1(x, y), x, inner_limit_low, inner_limit_high) * int(f2(x, y), x, inner_limit_low, inner_limit_high), y, 0, inf)

If it is able to perform the integral then unless there are additional symbolic variables that you have not mentioned, the result would be a symbolic number, not something you would typically plot() (except perhaps as a point.)

If the integral is determined to be not convergent then int() cannot always return a result that can be converted to a number.

If there is an additional symbolic variable such that result is a function, then plot(result) would be the wrong tool: you would use fplot() or you would use subs() specific values in for the variable and plot() the result.

[Walter Roberson]

In Maple notation, assuming that I is sqrt(-1), then

f1 := (y,x) -> exp(I*(x*sig_2*lamda_1+I*lamda_I1*alpha_1)*y/alpha_1);
f2 := (y,x) -> y+I*lamda_I3*alpha_1/(lamda_1*x*p_p);
f3 := (y,x) -> int(f1(x, y), x = I/p_umax .. infinity);
f4 := (y,x) -> int(f2(x, y), x = I/p_umax .. infinity);
f5 := y -> f3(y)*f4(y);
f6 := int(f5(y), y = 0 .. infinity);

and the result is

int((limit(alpha_1*(-exp((-I*lamda_I1*alpha_1-y*sig_2*lamda_1)/(p_umax*alpha_1))+exp(I*(y*sig_2*lamda_1+I*lamda_I1*alpha_1)*x/alpha_1))/(I*y*sig_2*lamda_1-lamda_I1*alpha_1), x = infinity))*infinity, y = 0 .. infinity)

which is to say the integral of infinity times a limit. The possible results of infinity times a limit are -infinity, +infinity, one of the complex infinities, or undefined (if it were infinity times 0)

If the equations are what you indicated then there would not appear to be a useful result.

[ASWATHI V]

So what can I do for getting a nmeical result?

[Walter Roberson]

If you indicate specific values for the variables then I can give a try. (Specific values help me choose the right range -- for example you might happen to know that all the values are positive, but with my not knowing that I might substitute negative values for sample coefficients and that might lead to a different set of problems.)

[ASWATHI V]

I = 1000;

sig_2 = 1;

P_p = 100;

lamda_1 = 1;

lamda_I1 = 1.5;

lama_I3 = 1.5;

alpha_1 = 0.3;

[ASWATHI V]

x from 0 to infinity

y from some value (it could be any positive value hich depends on so many other values, let it be 100) to infinity