HP 48G - And Integration

Implicit Differentiation
When unable to express y explicitly as a function of x,
try implicit means. Example: If x* + y*=9, find dy/dx.
First,purge '®' and '"'' fromthe current path. Next,
enter the equation—so that it says “y is a function of
x” TEMEHY TR 1*E=9" —then the variable, ', and
(@]3). Result: 'Z#A+der i, 112+ (H1=A" . The
expression detf' (¥, 11 means dy/dx, which you now
isolate: Editthe equation, replacmg-:ir—-r"lJ ¥ 10 with,
say, [ (and (1 with simply ). After substitution:
'y 2EY=R" Solve for 0Y: (" [a)B)a[Y)ENTER)
(lsymeouic) HENTMETRS. Result: 'D'Y=-(x-"1"
Partial Differentiation
The HP 48G/GX can take partial derivatives of multi-
variable functions. All variables except the variable of
differentiation are treated as constants (if you don'’t
express them as being functions of the variable of dif-
ferentiation—unlike implicit differentiation, above).
AND INTEGRATION
To compute an integral, you can use the J command
(via ([@)Y)), or Imt.=at-at 2. (under (>]sYMBOLIC).
Numeric Integration
1
Example: Find ,Jrl t. Try the EquationWriter,
+1?
0
which is very handy for integrals: Press
(0> [ENTER].
This puts 'J(H, 1, 1-C1+T*22, T1', the algebraic
form, onto the stack. Now press once to see the
integral before substituting numeric limits:
"TECATAMCT 2-aTCTaa 1 (T=12
—CL=CATAMCT 2aTCTad [ (T=R@21"
Use (EVALJagain until you geta numeric result (=. r254).
This is an exact integral, an explicit antiderivative, but
sometimes leaves an expression still containing
an integral (e.g. 'J(H, 1, e®=(H"21, K1'); the ma-
chine can’tfind an antiderivative. It knows antideriva-
tives for most built-in functions (and their derivatives),
and it automatically does simple linear substitutions,
but not much more. However, you can still get a good
result via numerical estimation....
24 THE HP 48G/GX Pocker GuIiDE