HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 301
Solution 1, Solution 2
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hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM Solution 1 Start by defining the following: g(x) = 2 - -----1-----x+2 Now type PROPFRAC(G(X)). Note that PROPFRAC can be found on the POLYNOMIAL submenu of the MATH menu. Pressing yields the result shown at the right. Solution 2 Enter the integral: 2 I = ∫ g(x)dx . 0 Pressing yields the result shown at the right: Pressing yields: again Step-by-Step Examples Working by hand: 2x + 3 = 2(x + 2) - 1 , so: g(x) = 2 - -----1-----x+2 Then, integrating term by term between 0 and 2 produces: ∫2 g ( x ) dx = [2x - ln(x + 2)] x = 2 0 x=0 that is, since ln4 = 2 ln2 : 2 ∫ g(x)dx = 4 - ln2 0 16-27
Step-by-Step Examples
16-27
Solution 1
Start by defining the
following:
Now type
PROPFRAC(G(X))
. Note
that
PROPFRAC
can be
found on the
POLYNOMIAL
submenu of the
MATH
menu.
Pressing
yields the
result shown at the right.
Solution 2
Enter the integral:
.
Pressing
yields the
result shown at the right:
Pressing
again
yields:
Working by hand:
, so:
Then, integrating term by term between 0 and 2
produces:
that is, since
:
gx
()
2
1
x
2
+
-----------
–
=
I
gx
()
x
d
0
2
∫
=
2
x
3
+
2
x
2
+
(
)
1
–
=
gx
()
2
1
x
2
+
-----------
–
=
gx
()
x
2
x
x
2
+
(
)
ln
–
[
]
=
d
0
2
∫
x
2
=
x
0
=
4
2
2
ln
=
ln
gx
()
x
4
2
ln
–
=
d
0
2
∫
hp40g+.book
Page 27
Friday, December 9, 2005
1:03 AM