HP 15c Scientific manual 8826, 7091

202 Section 14: Numerical Integration

If the uncertainty of an approximation is larger than what you choose to tolerate, you can decrease it by specifying a greater number of digits in the display format and repeating the approximation.*

Whenever you want to repeat an approximation, you don't need to key the limits of integration back into the X- and Y-registers. After an integral is calculated, not only are the approximation and its uncertainty placed in the X- and Y-registers, but in addition the upper limit of integration is placed in the Z-register, and the lower limit is placed in the T-register. To return the limits to the X- and Y-registers for calculating an integral again, simply press )).

Example: For the integral in the expression for J1(l), you want an answer accurate to four decimal places instead of only two.

Keystrokes	Display
´ i 4	1.8826	-03	Set display format to i4.
))	3.1416	00	Roll down stack until upper
			limit appears in X-register.
´f 1	1.3825	00	Integral approximated in
			i4.
®	1.7091	-05	Uncertainty of i
			4 approximation.

The uncertainty indicates that this approximation is accurate to at least four decimal places. Note that the uncertainty of the i 4 approximation is about one-hundredth as large as the uncertainty of the i 2 approximation. In general, the uncertainty of any f approximation decreases by about a factor of 10 for each additional digit specified in the display format.

*Provided that f(x) is still calculated accurately to the number of digits shown in the display.