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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 J

(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 i 4.

))

3.1416

Roll down stack until upper

limit appears in X-register.

´f 1

1.3825

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.

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