[2.10] Cas Square Root Simplification Limitations - Texas Instruments TI-89 Tip List

á(t^2*ℯ^(-s*t),t,0,∞)
If the mode is set to Rectangular or Real, undef is returned. If we constrain the soluton for s>0, like
this:
á(t^2*ℯ^(-s*t),t,0,∞)|s>0
but leave the complex format set to rectangular, the 89/92+ is 'busy' for a long time, then returns the
original integral. However, if we constrain the solution to s>0 and set the mode to Real, the calculator
quickly returns the correct answer: 2/s
Here is another integral that is sensitive to mode settings:
∞
¶
1
−∞
4✜ ( p 2 +z 2 ) 1.5
which is entered as
á(1/(4*Œ*(p^2+z^2)^(1.5)),z,-∞,∞)
I get these results on my TI-92 w/Pluse module, AMS 2.03. Real and Rectangular are the Complex
Format mode settings, and Exact and Approx are the Exact/Approx mode settings.
! Real, Exact: returns answer quickly
! Rectangular, Exact: returns answer, not as fast; warning message: "Memory full, some
simplification might be incomplete"
! Real, Approx: can't find integral
! Rectangular, Approx: can't find integral
Mode settings of Real, Exact seem to be the best starting point for symbolic integration.
So the moral of the story is this: if the 89/92+ won't evaluate your integral, try various complex modes
and constraints.
(I lost my note for the credit on this one. Sorry - it's a good one!)

[2.10] CAS square root simplification limitations

The 89/92+ CAS (computer algebra system) rarely treats the square root operator as identical to
raising the argument to the 1/2 power, because, in general, the two operations are not equivalent. For
example,
3
2 − x 3
x
does not simplify to zero. However, the expression does simplify to zero if we restrict x, in other words,
these expressions
3
2 − x 3 x x > 0
x
both correctly return zero.
3
.
1
dz =
2✜p 2
or
3
2 − x 3 x x m 0
x
2 - 5