9 replies to this topic

[verena]

A problem from a HP forum (and most HPs can't do it):
Solve t in [ {integral[sqrt(1+4x^2)]dx from 0 to t } = 6 ]
"sqrt" meaning "square root" and "4x^2" meaning "four times (x squared)"

The answer, t is about 2.306... (tried by hand, with the fx-4500P, guessing t repeatedly)
Can the fx-9860G solve this ?
I almost bought an fx-115MS or ES because they have Integrals and Solve, but then I saw in the online manual that "integrals cannot be used with Solve". duh.

However in the fx-9860G manual it only said that "solve cannot be used in integrals".

Would someone with an fx-9860G please define the integral [sqrt(1+4x^2)] dx from zero to t, and then run Solve" for t?

Thank you.

[Xerxes]

I have tried you problem on the FX-9860G. It's also not possible using integrals
in solve. So writing an own solve program is needed.

The TI-V200 is able to combine solve and integral thanks to CAS. The command
"solve(integral(sqrt(1+4x^2),x,0,t)=6,t)" gives t=2.30609738256 after about 110 sec.

[ECE]

Hello,
I tried to solve this problem using the numeric solver function in the ClassPad300;
[ {integral[sqrt(1+4x^2)]dx from 0 to t } = 6 ]with initial t=0 and boundaries (-∞,∞), the answer was t=2.306097383 and with the message ?there may exist more than one answer?.
I tried another technique, by first evaluating the integral y= {integral[sqrt(1+4x^2)]dx from 0 to t } the answer was y={[t*sqrt(4t^2+1)/2]+[ln(abs(8t+4* sqrt(4t^2+1)))/4]-[ln2/2]}, second I plot this function using the graph function and used the G-solve to find t when y=6, the answer was :
t=2.3060973 ?less precession than the first answer.
Xerxes: The ClassPad gave the answer for approximately 3 Sec. compared to 110 Sec. the TI-v200 is very slow! I was planning to buy a TI calculator, cause of its powerful CAS; but I didn?t knew its that slow.
What is the most powerful TI calc available in the market?
Inform me please.
Regards.

[kucalc]

That's weird... 3 secs on the ClassPad?

It takes the TI-nSpire CAS 5-6 seconds to solve that.

BTW, hello verena and welcome to the UCF!

[ECE]

That's weird... 3 secs on the ClassPad?

It takes the TI-nSpire CAS 5-6 seconds to solve that.

You are right , I recalculate using a stop watch several times with different initial values and the time was between 6sec to 6.3sec.

Note that I?m using O.S v3.03.

Thank you.

[Xerxes]

Please note that the speed difference of the CAS depends on the problem to solve and
maybe another type of problem runs much faster on the TI-V200.

I prefer the pen input of the ClassPad but the CAS of the TI(Derive).
If your priority is a good CAS and fast hardware then I'm in agreement
with CFX Master.

[ECE]

If your priority is a good CAS and fast hardware then I'm in agreement
with CFX Master.

yes, thanks to you and to CFX Master.

[DrCoyote]

Solving that takes about 3 seconds on my Ti-Nspire CAS. I'm running Version 1.3.2437.

I'll ask my friend to whom I sold my ClassPad to try this as well. She refuses to post here, so I'll pass along the results.

[verena]

I have tried you problem on the FX-9860G. It's also not possible using integrals
in solve. So writing an own solve program is needed.

The TI-V200 is able to combine solve and integral thanks to CAS. The command
"solve(integral(sqrt(1+4x^2),x,0,t)=6,t)" gives t=2.30609738256 after about 110 sec.

Thank you. Casio -1 for not mentioning it in the manual. I'm still not decided between an fx-9860 (it can't do that problem, but the Slim's backlight looks so nice) and the HP-50G (does so much more, faster, yet I fear the confusion).

[Xerxes]

IMHO the FX-9860GSD or the FX-9860G Slim are the best non CAS calculators at present.
Note that you can solve your given problem on this calculator, but you have to write
a program if you don't mind.

Of course the HP-50G or the TI-Nspire are the better choice, if you need CAS.