WP 34S integration accuracy

[Dieter]

(04-01-2015 05:55 PM)lrdheat Wrote:  I integrated e^(3x) * sin(4x) in fix 4 mode and got an instant result accurate to 3 significant digits. This surprised me as I expected at least 4 digit accuracy.

Indeed you get "4 digit accuracy" here. But not 4 significant digits. See below.

(04-01-2015 05:55 PM)lrdheat Wrote:  Then I had the vague recollection that for some problems where the area under the curve is quite small, the use of scientific notation would provide greater accuracy. Sure enough, in SCI 4, I get 9 significant digit accuracy.

Sure – this time you get five significant digits.

(04-01-2015 05:55 PM)lrdheat Wrote:  I'm wondering...is there a rule of thumb to go by as to how to choose the best entry mode for an integration?

There is a very simple rule: the iteration exits and the result is displayed as soon as the last two approximations agree when rounded to display precision.

This means that FIX 4 will yield a result that has four valid digits after the decimal point/comma. In your example the exact result is –0,0000141357... Already the first approximation yields –0,000014166. This agrees with the true result in even more than the first four digits: in FIX 4 both results would round to 0,0000 (!). Thus the iteration is considered converged, Integrate finishes and displays the result.

Now you said you want four significant (!) digits. This is what is displayed in SCI 3 mode. So set the 34s to SCI 3, try again and watch the iteration converge:
–1,417 E–5 ... –1,409 E–5 ... –1,414 E–5 ... and finally ∫=–1,414 E–5. Voilà.

Dieter