1. The TI-36X Pro (scientific calculator)

2. The Casio fx-115ES Plus (scientific calculator)

3. The Casio fx-991EX ClassWiz (scientific calculator)

4. The Casio fx-9860gii SD (graphing calculator)

5. The Casio fx-9750gii (graphing calculator)

6. The TI Nspire CX CAS (graphing calculator)

The problem used for test:

B = 1.3271244e+20

C = 6.957e+08

D = 1.495978707e+11

Evaluate:

∫ (C, 0.999999D) 1 / √(2B(1/x − 1/D)) dx

This integral returns the amount of time, in seconds, for an object to fall to the sun's photosphere (one solar radius = C) starting from a distance of 1 astronomical unit (D), assuming that the sun and the object are initially at rest with respect to each other and are acted upon by no forces other than their mutual gravitational attraction. The variable B is the solar gravitational parameter.

TI-36X Pro

Answer: 5570898.581

Time to Solve: 90.4 sec

Casio fx-115ES Plus

Answer: 5570898.583

Time to Solve: 76.6 sec

Casio fx-991EX ClassWiz

Answer: 5570898.583

Time to Solve: 17.3 sec

Casio fx-9860gii

Answer: 5570898.583

Time to Solve: 7.1 sec

Casio fx-9750gii

Answer: 5570898.583

Time to Solve: 4.9 sec

TI Nspire CX CAS

Answer: 5570898.58274

Time to Solve: 0.5 sec

As you can see, the TI-36X Pro is a slow-poke. The

**TI-36X Pro**costs anywhere from $19 to $30 on Amazon.

The

**Casio fx-991EX ClassWiz**is the official (and substantial) Casio upgrade to the earlier Casio fx-115ES Plus. For moderately complicated numerical integration chores, the Casio fx-991EX is more than four times faster than its predecessor model. Furthermore, the Casio fx-991EX is

*more than*than its ostensible competitor from Texas Instruments, the TI-36X Pro. The Casio fx-991EX sells at prices ranging from $14 to $36 on Amazon.

__five__times fasterBut the

**Casio fx-9750gii**is more than three times faster than the Casio fx-991EX ClassWiz and is about 18 times faster than the TI-36X Pro. Reasonable prices on Amazon go from $30 to $37, but there are some sellers (that should be ignored) who are trying to gouge for more.

The TI Nspire tops the list for speediness, however, being about ten times faster than even the Casio fx-9750gii, and it is 180 times faster than the slow-pokey TI-36X Pro.

I have solved the indefinite integral analytically. Omitting the intermediate steps,

∫ 1 / √(2B(1/x − 1/D)) dx

= √[D/(2B)] { √(XD−X²) + D arctan[√(D/X−1)] }

When I used the calculators to solve the integral numerically, I had to avoid entering D itself for x, since that would cause an overflow error. But in the analytical solution, when X=C, the answer is 5578001.670517. When X=0.999999D, the answer is 7103.088517. So the precise answer from the analytical solution, used twice to evaluate the integral from X=C to X=0.999999D, is 5570898.582. There is no appreciable error in the numerical results from any of the calculators.

**A Second Test of the Speediness of these six calculators, using a different numerical integration.**

The definite integral to be solved:

∫(0,6) exp(x³) dx

Casio fx-115ES Plus

Answer: 5.963938092e+91

Time to Solve: 120 sec

TI-36X Pro

Answer: 5.963938091e+91

Time to Solve: 81.5 sec

Casio fx-991EX ClassWiz

Answer: 5.963938092e+91

Time to Solve: 24.5 sec

Casio fx-9860gii:

Answer: 5.963938092e+91

Time to Solve: 6.5 sec

Casio fx-9750gii

Answer: 5.963938092e+91

Time to Solve: 5.8 sec

TI Nspire CX CAS

Answer: 5.9639380919e+91

Time to Solve: 0.7 sec

**A Third Test of the Speediness of these six calculators, using a different numerical integration.**

The definite integral to be solved:

∫(−5,99) ln(x²) dx

Casio fx-115ES Plus

Answer: 717.9281095

Time to Solve: 174 sec

TI-36X Pro

Answer: 717.9281268

Time to Solve: 61.5 sec

Casio fx-991EX ClassWiz

Answer: 717.9281095

Time to Solve: 35.0 sec

Casio fx-9860gii:

Answer: 717.9281095

Time to Solve: 8.2 sec

Casio fx-9750gii

Answer: 717.9281095

Time to Solve: 6.7 sec

TI Nspire CX CAS

Answer: 198 ln(99) + 10 ln(5) − 208

Answer equals: 717.9281095

Time to Solve: instant