HP 15c - Manual (Page 40)

40
Section 2:
Working with f
The HP-15C gives you the ability to perform numerical integration using f. This section
shows you how to use f effectively and describes techniques that enable you to handle
difficult integrals.
Numerical Integration Using
f
A calculator using numerical integration can almost never calculate an integral precisely. But
the f function asks you in a convenient way to specify how much error is tolerable. It asks
you to set the display format according to how many figures are accurate in the integrand
f(x). In effect, you specify the width of a ribbon drawn around the graph of f(x). The integral
estimated by f corresponds to the area under some unspecified graph lying entirely within
the ribbon. Of course, this estimate could vary by as much as the area of the ribbon, so f
estimates this area too. If I is the desired integral, then
















ribbon the
of area
2
1
ribbon the in drawn
graph a under area
I
The HP-15C places the first area estimate in the X-register and the second-the uncertainty-in
the Y-register.
For example, f(x) might represent a physical effect whose magnitude can be determined only
to within ± 0.005. Then the value calculated as f(x) has an uncertainty of 0.005. A display
setting of •2 tells the calculator that decimal digits beyond the second can't matter. The
calculator need not waste time estimating the integral with unwarranted precision. Instead,
the calculator can more quickly give you a fair idea of the range of values within which the
integral must lie.