Hello, everyone.

When I integrate I usually use my graphing calculator so I haven't encountered any obstacles/errors. My favorite scientific calculator (the calculator I always have with me everywhere I go) is HP 32sII, and recently I decided to use its numeric integration capability. Specifically I integrated the standard normal curve, exp^(-z^2/2)/sqrt(2*pi)--it produced inaccurate results using the EQN method, but produced accurate results using the PRGM method.

The expression I entered in EQN is exp^(-z^2/2)/sqrt(2*pi), and when I integrate it from z=0 to z=1, the result is 0.4767 (the correct result should be 0.3413). Integrating over smaller ranges (like z=0 to z=0.1, z=0 to z=0.5, etc), the error starts to accumulate.

I also integrated the standard normal curve by programming it:

A01 LBL A

A02 Ï€

A03 2

A04 Ã—

A05 SQRT

A06 1/x

A07 RCL Z

A08 x^2

A09 +/-

A10 2

A11 Ã·

A12 e^x

A13 Ã—

The results of integrating the PRGM above of the standard normal curve are accurate.

I tried inputting the EQN and PRGM in HP 33s and HP 35s and the results are accurate.

I guess that's one of the reasons why the HP32sII was discontinued and better versions were conceived. It's a shame really, HP 32sII is the best among the last 3 great scientific calculators (HP 32sII, HP 33s, HP35s) that HP produced. HP 32sII has floating comma when inputting numbers, unlike the HP 35s. Number crunching is crisper in the 32sII, there's no worry that some buttons may not have registered (*cough* HP 35s *cough*), there's a large ENTER button unlike the miniscule ENTER button on the 33s. Entry of simple fractions, for example 3/4, is 3-decimal-decimal-4, not decimal-3-decimal-4 that 35s requires. Everything is so fluid in the HP 32sII...Ahh, sorry for the short spiel there, I'm just so passionate about the 32sII. :)

As a business-related student I use a financial calculator, too (HP 10bII+), and it has a "Z<>P" capability that converts z-scores to probabilities/areas under the standard normal curve, so I'm not that too hampered by my HP32sII's shortcomings, integration-wise.

Now that I'm on the topic of financial calculators, HP SHOULD MAKE a hybrid of HP32sII and HP 10bII+, an RPN scientific/financial calculator in which all the functions are accessible through the shift keys as opposed to having to invoke a menu to access such math functions like LOG. I love RPN, but I didn't gravitate towards the HP 30b when selecting my financial calculator because of that nuisance: in order to use the math functions like LOG, LN, etc, one would have to go through a menu. Oh, well.

Well, I just wanted to share the error in the HP 32sII to make everyone aware of its inaccurate integration of the standard normal curve.

Thanks.