HP 48G - Page 27

Example: Repeatthe above example, but use ]-Num]
instead of (EVAL. Note the appearance of HITIH in
the VAR menu. The number in IERR is a likely bound
on the maximum error in the estimated integral; the
accuracy is set by the display mode: More digits offer
more accuracy (andincreased calculation time). Com-
pare results with a display set to STD, then FIX 2.
To evaluate a multiple integral, key it in just as you
would write it—one integral nested inside the other—
and, again, the EquationWriter is handy for entering.
4
Example: _J J 2xy dy dx
0¥l
Then use or(EVAL) as usual (though you may
need more repetitions of (or even EXPAND and
COLCT) to get a final explicit result if indeed possible.
To evaluate an improper integral (where the limits
may be infinite), change variables. If x is unbounded,
one handy transformation is w =tan"'x. Then tan'(xeo)
= +71/2, and fix)dx = f(tanw)(1+tan’w)dw.
Symbolic Integration
. Xl . 1T 1
Example: Integrate J — du. First,purge T' and'#
t
1
from the current path, then use and se-
lect Int.earate.. Put'1-T' in ExPR:, T invak:,
linLD: and ¥ inHi:. SetkESULT: to'Sumbaol ic, and
Il Result: '1#(LNCT)-aTCTII(T=H)-(1%
CLMCT2-aTCTaXI(T=12)". Press(EvAL: 'LMCx2!
Example: Find the antiderivative of 3(x+5)>. Purge
'"H' from the current path, then use and
select Imt. egr-at. ... Enter ' 3#(¥+0)"2 " in EXPER:,
& inwak:, B inLD: and B inHE. Put Sumbiol 1 into
the REZULT: field, and press IITHM. Result:
"R CRADIMEHL D CCE+] DRI+ ) [ (R=H)
=3 ORI (241 0 (O 1R (H+000 ) | C=H00 1
Now, don’t press yet. First, discard the second
part of this result—that for the zero lower limit:
I [EFEN (GROPIDROPIDROP). Now press (EVAL.
Result: ' 3*((#¥+51*3-31" (Youcan further simplify
this via [F{ZLY and from (€]SYMBOLIC).)
These examples work because their integrands have
easy antiderivatives. For an integrand that doesn’t,
you can get a symbolic approximation: Integrate the
Taylor polynomial approximation of the integrand.
and Integration 25