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A More Detailed Look at ()
267
tainty of the total approximation is not appreciably larger than the
uncertainty of the single approximation over the entire interval.
Transformation of Variables
In many problems where the function changes very slowly over most of a
very wide interval of integration, a suitable transformation of variables
may decrease the time required to calculate the integral.
For example, consider again the integral
*
f xe ™ dx.
0
Let
u=e>x.
Then
x=—"lnu
and
dx = — fll—
u
Substituting,
J'Oxxe'xdx =fe:~x(— Inu) (u) (— d7u>
=f10 In u du.
Slide the PRGM-RUNswitchto prem [l and key in a subroutine that
evaluates the function f(u) = In u.
Keystrokes
Display
)
3
001- 25,13, 3
(]
002-
14 1
M EN
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