How to evaluate an integral?

Hello,

I would like to evaluate the following function which includes an integral. The aim is to get sth. like that: Var_beta_hat_direct = a kind of number. But I only get a symbolic expression and not a number.

Does anybody have an idea?

syms t

Var_beta_hat_direct=vpa(10681743549394799937933824491520*exp(int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(4831891999187463/1125899906842624))*exp(8187485477687969/1715238139330560)*((140737488355328*exp(-int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(4831891999187463/1125899906842624))*exp(-8187485477687969/1715238139330560)*int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(3705992092344839/1125899906842624))/8301382342175545 + (690270285598209*log(int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944))*exp(-int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(4831891999187463/1125899906842624))*exp(-8187485477687969/1715238139330560)*int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(3705992092344839/1125899906842624))/9487294105343480 - (690270285598209*log(int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944))*exp(-int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(4831891999187463/1125899906842624))*exp(-8187485477687969/1715238139330560)*int((140737488355328*exp(-8187485477687969/(4398046511104*(20*heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944)^(4268942045766151/562949953421312))/9487294105343480))

Answer 1

[Walter Roberson]

All of those int() expressions are exactly the same. Pull that out of the expression and evaluate it and drop the result into the larger expression.

The result is about -2.546320960311438*10^28 by the way.

[Max]

Hello Walter,

first of all, thank you for your answer. I tried out your approach but I can´t get a result for the integral which repeats up to 9 times. My code is looking like that:

I=vpa(int((140737488355328*...
    exp(-8187485477687969/(4398046511104*(20*...
    heaviside(t - 2000) + 40*heaviside(t - 3000) - 390*heaviside(t - 14000) + 330*heaviside(t)))))/8301382342175545, t, 0, 1671787363946201/274877906944));

Can you tell me where the error occurred?

[Walter Roberson]

What result do you get for that?

The Maple based symbolic toolbox that I am using gives 0.6449536423

By the way, since you are looking for a numeric value, you should use double() instead of vpa()

[Max]

That´s the problem. If I use double() then I´ll get:Error using symengine DOUBLE cannot convert the input expression into a double array. If the input expression contains a symbolic variable, use VPA.

[Walter Roberson]

What is the result you get with vpa() ?

[Max]

If I use vpa() then I´ll get: numeric::int((140737488355328*exp(-8187485477687969/(87960930222080*heaviside(t - 2000) + 175921860444160*heaviside(t - 3000) - 1715238139330560*heaviside(t - 14000) + 1451355348664320*heaviside(t))))/8301382342175545, t == 0..6082)

[Walter Roberson]

Odd, I cannot see any reason at the moment why a numeric integration of that might fail.

Which MATLAB version are you using? If you are using R2015a or later I suggest you experiment with using sympref to give a definite numeric value to heaviside(0)

[Max]

I´m using the R2015b version.

[Max]

But you also can test out my code and you´ll see that it´s not working.