Section 14: Numerical Integration 195
Key the lower limit of integration (a) into the X-register, then press
v to lift it into the Y-register.
Key the upper limit of integration (b) in to the X-register.
Press ´ f followed by the label of your subroutine.
Example: Certain problems in physics and engineering require calculating
Bessel functions. The Bessel function of the first kind of order 0 can be
expressed as


Ï€
0
0
)sin ( cos
Ï€
1
)( dθθxxJ


Ï€
0
0
)(sin cos
Ï€
1
(1) dθθJ
.
In Program mode, key in the following subroutine to evaluate the function
f(θ) = cos (sin θ).
Begin subroutine with a
b instruction.
Subroutine assumes a
value of θ is in X-register.
Now, in Run mode key the lower limit of integration into the Y-register and
the upper limit into the X-register. For this particular problem, you also
need to specify Radians mode for the trigonometric functions.