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D–4 More about Integration
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
∫
∞
−
0
dxxe
x
Since you're evaluating this integral numerically, you might think that you
should represent the upper limit of integration as 10
499
, which is virtually the
largest cumber you ears key into the calculator.
Try it and what happens. Enter the function f(x) = xe
–x
.
Keys: Display: Description:
{
G
Select equation mode.
K
X
y
*
%º%1¾
Enter the equation.
K
X
{
]
%º%1.%2
End of the equation.
{
/
)
Checksum and length.
Cancels Equation mode.
Set the display format to SCI 3, specify the lower and upper limits of
integration as zero and 100
499
, than start the integration.
Keys: Display: Description:
z
{
} 3
0
`
499
_
Specifies accuracy level and
limits of integration.
{
G
%ºº1.%2
Selects Equation mode; displays
the equation.
{
)
X
!!
∫
/)
Approximation of the integral.
The answer returned by the calculator is clearly incorrect, since the actual
integral of f(x) = xe
–x
from zero to
∞
is exactly 1. But the problem is not that
∞
was represented by 10
499
, since the actual integral of this function from
zero to 10
499
is very close to 1. The reasons or the incorrect answer becomes
apparent from the graph of f(x) over the interval of integration.