Is there any way of applying the romberg (or other numeric) method to a definite integral embedded in an expression?
When wxMaxima fails to find a closed form solution, as in:
f(x):=sin(%e^x)/x^2; integrate(f(x),x,1,2);
one is left with an expressioin that includes the integrate symbol with the definite integral bounds.
Of course, if one attempts:
romberg(%);
one gets the error message:
romberg: wrong number of arguments.
rather than the desired:
romberg(f(x),x,1,2); −0.14527907494713
load(romberg)$ f(x):=sin(%e^x)/x^2$ romberg(f(x), x, 1, 2);
f(x):=sin(%e^x)/x^2; integrate(f(x),x,1,2); apply(romberg, args(%));
Does this do what you want? However, romberg must have been loaded. Otherwise:
a: args(%); load(romberg); apply(romberg, a);
That's a beautiful solution, Franz. If one were going to use it repeatedly, then it might even be phrased as a function to save some typing:
numeric(x):=apply(romberg,args(x));
After a symbolic integration fails, then one could simply type:
numeric(%)
By the way, in the Windows version, I find that romberg() is loaded by default, cutting down even further on the typing.
Is there any way of applying the romberg (or other numeric) method to a definite integral embedded in an expression?
When wxMaxima fails to find a closed form solution, as in:
one is left with an expressioin that includes the integrate symbol with the definite integral bounds.
Of course, if one attempts:
one gets the error message:
rather than the desired:
Last edit: Jim Bowery 2015-11-26
load(romberg)$
f(x):=sin(%e^x)/x^2$
romberg(f(x), x, 1, 2);
f(x):=sin(%e^x)/x^2;
integrate(f(x),x,1,2);
apply(romberg, args(%));
Does this do what you want? However, romberg must have been loaded. Otherwise:
a: args(%);
load(romberg);
apply(romberg, a);
That's a beautiful solution, Franz. If one were going to use it repeatedly, then it might even be phrased as a function to save some typing:
numeric(x):=apply(romberg,args(x));
After a symbolic integration fails, then one could simply type:
numeric(%)
By the way, in the Windows version, I find that romberg() is loaded by default, cutting down even further on the typing.