All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
Getting Natural With Sine (Posted on 2009-05-19) Difficulty: 2 of 5
Evaluate:

pi/2
sin y*ln(sin y) dy
0

where, ln y denotes the natural logarithm of y.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts numerical integration with computer--but what is this number? | Comment 1 of 3

DEFDBL A-Z
pi = ATN(1) * 4
incr = .0000001#
FOR y = incr / 2 TO pi / 2 STEP incr
 t = t + SIN(y) * LOG(SIN(y))
NEXT
PRINT t * incr

Successively changing the increment from .0001 to .0000001 by dividing by 10 each time produces

-.3068528238160199
-.3068528194936749
-.3068528194417146
-.3068528194866375

I have the feeling that the changeover from decreasing to increasing in the last instance is the result of more terms being added, and therefore producing lower, rather than higher, accuracy. On that basis, I'd limit the quoted value accuracy to -.3068528194....

UBASIC, with higher precision can be used:

10         Incr=0.0000001
15          Y=Incr/2
20          loop
30               T=T+sin(Y)*log(sin(Y))
35               Y=Y+Incr
36               if Y>#pi/2 then goto 50
40          endloop
50         print T*Incr

giving -0.306852819440061945, so I would feel safe with the accuracy of -0.30685281944.

 


  Posted by Charlie on 2009-05-19 12:28:29
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information