10-23-2021, 11:46 AM

In the HP35S manual at E-3 there is a workaround attempting to solve the infamous integral "∫ from 0 to ∞ of the expression xe^-x", but the proposed solution to change ∞ with 10E3 is far from ideal.

This short program is inspired by "Tips and Programs for the HP-32S"" published by Synthetix in 1988.

This program turns the original integral:"∫ from a to b of f(x) dx"

Into a new: "∫ from ATANa to ATANb of f(TANθ)/COS^2(θ) dθ"

so you can enter π/2 instead of +∞ and -π/2 instead of -∞.

It assumes that LBL F is dedicated to the function to be integrated.

LINE INSTRUCTION

I001 LBL I

I002 (MODE) RAD

I003 RCL X

I004 ENTER

I005 COS

I006 X^2

I007 X=0?

I008 RTN

I009 STO A

I010 X<>Y

I011 TAN

I012 STO X

I013 XEQ F001

I014 RCL A

I015 /

I016 RTN

INSTRUCTIONS:

1. Enter the function in LBL F (as EQN or in RPN. Please take into account that EQN mode is more visual appealing, but RPN mode is approx. 30% faster.

2. Input lower limit in RAD, press ENTER, and input upper limit in RAD.

3. Press FN= I ∫ , chose x to integrate, and wait patiently for the answer.

NOW YOU CAN EASILY SOLVE THE INFAMOUS INTEGRATION WITH THE INFINITE LIMIT "∫ from 0 to ∞ of the expression xe^-x":

1. Enter in LBL F the expression as: LBL F, RCL X, ENTER, +/-, e^x, *, RTN.

2. Enter 0 as lower limit, and press π, 2, / as upper limit.

3. Press FN= I ∫ , chose x to integrate, and you obtain in less than 3 minutes the right answer "1".

If you need to integrate from an arbitrary "a" , just input atan(a) insted of a, and if you are not in RAD mode, remember to press →RAD. (ex. from 2 to infinite, instead of just pressing 2, press 2 and ATAN if you are already in RAD mode, otherwise press 2, ATAN and →RAD.

IMPORTANT NOTE: the program switches to RAD mode. Remember to restore DEG mode if you use your calculator this way.

Enjoy!

This short program is inspired by "Tips and Programs for the HP-32S"" published by Synthetix in 1988.

This program turns the original integral:"∫ from a to b of f(x) dx"

Into a new: "∫ from ATANa to ATANb of f(TANθ)/COS^2(θ) dθ"

so you can enter π/2 instead of +∞ and -π/2 instead of -∞.

It assumes that LBL F is dedicated to the function to be integrated.

LINE INSTRUCTION

I001 LBL I

I002 (MODE) RAD

I003 RCL X

I004 ENTER

I005 COS

I006 X^2

I007 X=0?

I008 RTN

I009 STO A

I010 X<>Y

I011 TAN

I012 STO X

I013 XEQ F001

I014 RCL A

I015 /

I016 RTN

INSTRUCTIONS:

1. Enter the function in LBL F (as EQN or in RPN. Please take into account that EQN mode is more visual appealing, but RPN mode is approx. 30% faster.

2. Input lower limit in RAD, press ENTER, and input upper limit in RAD.

3. Press FN= I ∫ , chose x to integrate, and wait patiently for the answer.

NOW YOU CAN EASILY SOLVE THE INFAMOUS INTEGRATION WITH THE INFINITE LIMIT "∫ from 0 to ∞ of the expression xe^-x":

1. Enter in LBL F the expression as: LBL F, RCL X, ENTER, +/-, e^x, *, RTN.

2. Enter 0 as lower limit, and press π, 2, / as upper limit.

3. Press FN= I ∫ , chose x to integrate, and you obtain in less than 3 minutes the right answer "1".

If you need to integrate from an arbitrary "a" , just input atan(a) insted of a, and if you are not in RAD mode, remember to press →RAD. (ex. from 2 to infinite, instead of just pressing 2, press 2 and ATAN if you are already in RAD mode, otherwise press 2, ATAN and →RAD.

IMPORTANT NOTE: the program switches to RAD mode. Remember to restore DEG mode if you use your calculator this way.

Enjoy!