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I found an interesting set of integrals in the book "Inside Interesting Integrals" by Paul J. Najin. The author shows a set of integral in the preface section:

int(cos(x)*sin(4*x)/x,x,0,infinity)
int(cos(x)*cos(x/2)*sin(4*x)/x,x,0,infinity)
int(cos(x)*cos(x/2)*cos(x/3)*sin(4*x)/x,x,0,infinity)

and so an. Interestingly, each of the above integrals evaluates to pi/2. I tried to evaluate the integral int(cos(x)*cos(x/2)*sin(4*x)/x,x,0,infinity) (I am writing it using HP Prime form) with the Casio fx-CG500, but the calculator just kept on computing! I tried the same integral with the HP Prime which promptly returned a pretty version on the integral. Subtle AND polite!

I then tried int(cos(x)*cos(x/2)*sin(4*x)/x,x,0,1000*pi) on the HP Prime and instantly obtained 1.57061752887. I tried the same with the Casio ... which kept on calculating!!! It took the DM-15L just about 2 minutes to match the result of the HP Prime.

I am disappointed with the Casio fx-CG500. Good job HP ... at least for the approximation of the integral's limit.

Namir
(09-01-2017 08:12 PM)Namir Wrote: [ -> ]I found an interesting set of integrals in the book "Inside Interesting Integrals" by Paul J. Najin. The author shows a set of integral in the preface section:

int(cos(x)*sin(4*x)/x,x,0,infinity)
int(cos(x)*cos(x/2)*sin(4*x)/x,x,0,infinity)
int(cos(x)*cos(x/2)*cos(x/3)*sin(4*x)/x,x,0,infinity)

and so an. Interestingly, each of the above integrals evaluates to pi/2. I tried to evaluate the integral int(cos(x)*cos(x/2)*sin(4*x)/x,x,0,infinity) (I am writing it using HP Prime form) with the Casio fx-CG500, but the calculator just kept on computing! I tried the same integral with the HP Prime which promptly returned a pretty version on the integral. Subtle AND polite!

I then tried int(cos(x)*cos(x/2)*sin(4*x)/x,x,0,1000*pi) on the HP Prime and instantly obtained 1.57061752887. I tried the same with the Casio ... which kept on calculating!!! It took the DM-15L just about 2 minutes to match the result of the HP Prime.

I am disappointed with the Casio fx-CG500. Good job HP ... at least for the approximation of the integral's limit.

Namir
These integrals also lock up my TI Nspire CX CAS. Well, there is a key combination to interrupt the calculation, but it seems to automatically restart the calculation afterwards. I had to use the reset button on the back!
(09-01-2017 09:56 PM)ijabbott Wrote: [ -> ]These integrals also lock up my TI Nspire CX CAS. Well, there is a key combination to interrupt the calculation, but it seems to automatically restart the calculation afterwards. I had to use the reset button on the back!

Did you get a result on the TI NSpire?

Namir
How about this integral I try on HP Prime App, HP 15C App for Android and HP 15C Virtual Calculator for Windows PC.

1. HP Prime App gave error message then gave correct result.
2. HP 15C App for Android crash and close the app.
3. HP 15C Virtual Calculator ran smoothly and took about almost 1 minute.

The Casio Classwiz 911EX emulator ran about 20 second with correct answer.

Here is the attach jpg for this integral problem.

Gamo
(09-01-2017 11:38 PM)Namir Wrote: [ -> ]
(09-01-2017 09:56 PM)ijabbott Wrote: [ -> ]These integrals also lock up my TI Nspire CX CAS. Well, there is a key combination to interrupt the calculation, but it seems to automatically restart the calculation afterwards. I had to use the reset button on the back!
Did you get a result on the TI NSpire?

No, I didn't. In "Approximate" mode it just goes forever. In "Exact" mode it just spits back the same integral.

For nInt(cos(x)*sin(4*x)/x, x, 0, 1000*pi), it did give an answer of 1.57071144416, but it took about 3m50s to do so!

For Gamo's integral, nInt(e^(x^3),x,0,6), it gave an answer of 5.9639380919e91 within a fraction of a second.

(I think the problem I had with it automatically restarting the calculation was some strange loop it got into as a result of me mashing the buttons. If you just hold down the "Home" button for a couple of seconds, it breaks out cleanly.)
(09-02-2017 01:34 AM)Gamo Wrote: [ -> ]How about this integral I try on HP Prime App, HP 15C App for Android and HP 15C Virtual Calculator for Windows PC.