# integrating a hyperbola

• July 19th, 2014, 12:07 AM
whizkid
integrating a hyperbola
I have done this integration at Wolfram:
http://www.wolframalpha.com/input/?i...rom+0+to+995++
it gives a result but says computation time exceeded
If you have access to a good math program, can you check if the rsult is correct?
Thanks
• July 19th, 2014, 04:05 AM
MagiMaster
Mathematica gives the same answer (unsurprisingly). The "time limit exceeded" just means it ran out of time to do all the other things Alpha will try and do with your expression. If it ran out of time on the main result (which certainly can happen), it wouldn't give you one at all.
• July 19th, 2014, 07:14 AM
whizkid
Thanks Magimaster,
since you are an expert, can you explain what is (if any) the practical rule to find quicly the result.
To simplify matters I have changed the parameters:
integrate y= sin(tan^-1(5/x))* 50000/ (x^2+25) from 0 to 1 - Wolfram|Alpha

I tried to deduce it from the indefinite integral, but did not succeed:

from 0 to 1 = 5000 sqrt(2/13)
from 0 to 2 = 20000/sqrt29
from 0 to 5 = 5000 sqrt2
from 0 to 10 = 4000 sqrt5
from 0 to 1000 = 2 000 000/sqrt 40 001

why sometimes the sqrt is above and sometimes is below?
• July 19th, 2014, 01:56 PM
MagiMaster
You should probably put the square root around the whole thing ( and ).

When you say quickly find the result, do you mean "quickly find the definite integral given the indefinite integral," or "quickly find the indefinite integral," or something else? If it's the first, then call the indefinite integral . Then the definite integral . If it's the second, there's no quick way of working out integrals.
• July 20th, 2014, 01:30 AM
Markus Hanke
Works perfectly fine on my iMac, both in WolframAlpha and in MAPLE. This ( rather complicated ) definite integral evaluates to 10768.4
• July 20th, 2014, 05:35 AM
whizkid
Quote:

Originally Posted by Markus Hanke
Works perfectly fine on my iMac, both in WolframAlpha and in MAPLE. This ( rather complicated ) definite integral evaluates to 10768.4

It is not so complicated after all Markus, it boils down to k sin^3
if x and 4.64.. are the legs of a triangle