HP 40gs User Manual page 301

Step-by-Step Examples
Solution 1
Start by defining the
g x ( )
=
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:
2
∫
g x ( ) x d
I =
.
0
Pressing yields the
result shown at the right:
Pressing again
yields:
Working by hand:
( ) 1
2x + 3 = 2 x + 2
Then, integrating term by term between 0 and 2
produces:
2
∫
g x ( ) x [
d = 2x
0
ln 4
that is, since
2
∫
g x ( ) x
d = 4 –
0
1
----------- -
2 –
x + 2
g x ( )
– = 2
, so:
x =
( ) ]
– ln x + 2
x =
= 2 2 ln
:
ln 2
1
----------- -
–
x + 2
2
0
16-27