HP 15c Scientific manual Keys lower limit into, Keys upper limit into, Approximation to integral

	Appendix E: A Detailed Look at f 255
Keystrokes	Display
0 v	0.000	00	Keys lower limit into
			Y-register.
‛ 3	1	03	Keys upper limit into
			X-register.
´ f 1	1.000	00	Approximation to integral.
®	1.824	-04	Uncertainty of
			approximation.

This is the correct answer, but it took almost 60 seconds. To understand why, compare the graph of the function over the interval of integration, which looks about identical to that shown on page 252, to the graph of the function between x = 0 and x = 10.

By comparing the two graphs, you can see that the function is "interesting" only at small values of x. At greater values of x, the function is "uninteresting," since it decreases smoothly and gradually in a very predictable manner.

As discussed earlier, the f algorithm will sample the function with higher densities of sample points until the disparity between successive approximations becomes sufficiently small. In other words, the algorithm samples the function at increasing numbers of sample points until it has sufficient information about the function to provide an approximation that changes insignificantly when further samples are considered.