|Re: Symbolic integration on HP48GX|
Message #2 Posted by Reinhard Hawel on 1 Feb 2000, 9:27 p.m.,
in response to message #1 by Aldo
I know, that I'm in danger making myself completely ridiculous with answering in such a thread, but anyway, I just can't resist.
First the solution: (I'll write the integral sign as an upper-case I here.)
I sin(x) * cos(x) * dx
with: I u * dv = u * v - I v * du i'll write
u = sin(x) => du = cos(x) * dx dv = cos(x) * dx => v = sin(x)
I sin(x) * cos(x) * dx = sin(x) * sin(x) - I cos(x) * sin(x) *dx
rearranging the right Integral gives:
I sin(x) * cos(x) * dx = sin(x) * sin(x) - I sin(x) * cos(x) *dx
I add I sin(x) * cos(x) *dx to both sides of the equation.
2 * (I sin(x) * cos(x) * dx ) = sin(x) * sin(x)
which leads to
I sin(x) * cos(x) * dx = ( sin(x) * sin(x) ) / 2
I hope this formats well on the forum.
I don't have my 48GX manual handy, but the 48 SX manual says, thet the calculator compares PATTERNS of math strings for integration. This makes clear, that it does integration of polynomials (a rather easy task) or simple (even nested) functions, but no substitutions like the one above.
I'm pretty sure, that Derive has a better engine for integrating symbolic expressions than the 48.
The 48SX manual even gives an example of an expression, that can't be integrated, but can be formed, so that integration is possible after some operations. (I have the German version, your's might differ, my fellow Americans)
I fear, there's no way around learning such things the hard way (with lot's of integrals solved by hand) and even then, there's not always the right (or right formulated) result.
Just take it easy. Did you ever try to make a back-transformation of a Z-transformed expression ? Such things are common in communications engineering and the solution approach can get rather tricky (and the calculations can get rather long).
BTW: did anybody try this on a TI-92 ? I read somewhere, their Software is written by the Derive guys.