Attached integral calculator cannot solve
11-15-2019, 11:15 AM
Post: #1
 yingwuluo Junior Member Posts: 32 Joined: Aug 2017
Attached integral calculator cannot solve
Attached integral calculator cannot solve

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11-15-2019, 11:49 AM
Post: #2
 Gerson W. Barbosa Senior Member Posts: 1,584 Joined: Dec 2013
RE: Attached integral calculator cannot solve
Have you tried numerical integration? No Prime here, but on the HP 50g we can do

'∫(-2,2,(X^3*COS(X/2)+1/2)*√(4-X^2),X)'

→NUM

3.14159265359
11-15-2019, 12:05 PM
Post: #3
 Aries Member Posts: 159 Joined: Oct 2014
RE: Attached integral calculator cannot solve
CX II yields the same result (that is pi), try numerical mode as mentioned

11-15-2019, 12:56 PM
Post: #4
 Werner Senior Member Posts: 881 Joined: Dec 2013
RE: Attached integral calculator cannot solve
You just have to realise that

'∫(-2,2,(X^3*COS(X/2)+1/2)*√(4-X^2),X)'
= '∫(-2,2,X^3*COS(X/2)*√(4-X^2),X)' + '∫(-2,2,1/2*√(4-X^2),X)'

The first part is an odd function, so the integral is zero, and we are left with the easy second part.

Cheers, Werner

41CV†,42S,48GX,49G,DM42,DM41X,17BII,15CE,DM15L,12C,16CE
11-15-2019, 01:30 PM
Post: #5
 rombva Junior Member Posts: 38 Joined: Oct 2019
RE: Attached integral calculator cannot solve
(11-15-2019 11:15 AM)yingwuluo Wrote:  Attached integral calculator cannot solve

numerically: int((x^3*cos(x/2)+1/2)*√(4-X^2),x,-2,2) [shift] [enter] returns 3.14159265359.

symbolically: simplify(subst(int((x^3*cos(x/2)+1/2)*√(4-X^2),x,-2,2), x=2*sin(t))) returns pi.
11-15-2019, 02:04 PM
Post: #6
 rprosperi Super Moderator Posts: 6,295 Joined: Dec 2013
RE: Attached integral calculator cannot solve
With that answer, to access the WiFi network, do you suppose the 10th digit should be a 3 or a 4 ? Setting a calculator to Fix 9 would lead most folks to use the 4, while the 10th digit actually is 3. Not sure what the network admin had in mind. Who would guess that numerical rounding rules would need to be specified for a WiFi password?

--Bob Prosperi
11-15-2019, 02:20 PM
Post: #7
 toml_12953 Senior Member Posts: 2,103 Joined: Dec 2013
RE: Attached integral calculator cannot solve
(11-15-2019 11:15 AM)yingwuluo Wrote:  Attached integral calculator cannot solve

It works for me:

Tom L
Cui bono?
11-15-2019, 02:25 PM
Post: #8
 Albert Chan Senior Member Posts: 2,611 Joined: Jul 2018
RE: Attached integral calculator cannot solve
(11-15-2019 12:56 PM)Werner Wrote:  You just have to realise that

'∫(-2,2,(X^3*COS(X/2)+1/2)*√(4-X^2),X)'
= '∫(-2,2,X^3*COS(X/2)*√(4-X^2),X)' + '∫(-2,2,1/2*√(4-X^2),X)'

The first part is an odd function, so the integral is zero, and we are left with the easy second part.

To finish, second part = ½ area of half-circle (radius 2) = ½ (2 pi) = pi

(11-15-2019 02:04 PM)rprosperi Wrote:  With that answer, to access the WiFi network, do you suppose the 10th digit should be a 3 or a 4 ?

That implied round-toward-zero ⇒ password = 3141592653
11-15-2019, 02:42 PM
Post: #9
 toml_12953 Senior Member Posts: 2,103 Joined: Dec 2013
RE: Attached integral calculator cannot solve
(11-15-2019 02:25 PM)Albert Chan Wrote:
(11-15-2019 12:56 PM)Werner Wrote:  You just have to realise that

'∫(-2,2,(X^3*COS(X/2)+1/2)*√(4-X^2),X)'
= '∫(-2,2,X^3*COS(X/2)*√(4-X^2),X)' + '∫(-2,2,1/2*√(4-X^2),X)'

The first part is an odd function, so the integral is zero, and we are left with the easy second part.

To finish, second part = ½ area of half-circle (radius 2) = ½ (2 pi) = pi

(11-15-2019 02:04 PM)rprosperi Wrote:  With that answer, to access the WiFi network, do you suppose the 10th digit should be a 3 or a 4 ?

That implied round-toward-zero ⇒ password = 3141592653

Statisticians either round half to even or round half to odd:

Round half to even:
1.235 ==> 1.24
1.245 ==> 1.24
1.255 ==> 1.26
1.265 ==> 1.26

Round half to odd:
1.225 ==> 1.23
1.235 ==> 1.23
1.245 ==> 1.25
1.255 ==> 1.25

This way the rounding error is minimized in large populations of data.

Tom L
Cui bono?
11-15-2019, 07:02 PM
Post: #10
 lrdheat Senior Member Posts: 856 Joined: Feb 2014
RE: Attached integral calculator cannot solve
Just for the fun of it, I tried the definite integral on my CASIO fix-991EX, and it came up with the symbol for pi!
11-16-2019, 03:13 AM
Post: #11
 rprosperi Super Moderator Posts: 6,295 Joined: Dec 2013
RE: Attached integral calculator cannot solve
(11-15-2019 07:02 PM)lrdheat Wrote:  Just for the fun of it, I tried the definite integral on my CASIO fix-991EX, and it came up with the symbol for pi!

Well... that's only 2 digits! No WiFi for you!

--Bob Prosperi
11-16-2019, 04:35 PM
Post: #12
 lrdheat Senior Member Posts: 856 Joined: Feb 2014
RE: Attached integral calculator cannot solve
Seinfeld! Quotable for almost every aspect of life!
11-16-2019, 04:57 PM
Post: #13
 dan_h Junior Member Posts: 27 Joined: Feb 2014
RE: Attached integral calculator cannot solve
Using Mathematica Home Edition 12.0, it took a little longer than usual with other equations but finally produced the Pi symbol. On my G2 it returned the equation unsolved, but when I hit Simplify, it returned Pi.
11-16-2019, 07:35 PM (This post was last modified: 11-18-2019 02:14 PM by swagner53.)
Post: #14
 swagner53 Junior Member Posts: 18 Joined: Jun 2018
RE: Attached integral calculator cannot solve
The Prime G1 had no problem coming up with the Pi symbol in CAS or 3.141592... in Home right away. Odd thing was both worked straight off using lowercase x, then when I tried later in Home received an "Error: Syntax Error" message until I changed to an uppercase X. Took 1.034_s in CAS and .588_s in Home.

BTW, also tried solving in Mathematica 12 Home Edition on an 8-core, 64 GB RAM PC with 2 TB SSD. It took .656 seconds to return the Pi symbol, slightly longer than the HP Prime G1 in Home mode.
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