I found this one on a Harvard graduate level exam:

http://img206.imageshack.us/img206/9027/toughqj9.png

Any clues?

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- Dec 27th 2008, 11:37 AMRedBarchettaTougher Integral
I found this one on a Harvard graduate level exam:

http://img206.imageshack.us/img206/9027/toughqj9.png

Any clues? - Dec 27th 2008, 11:48 AMJester
- Dec 28th 2008, 01:05 AMpberardi
Could someone kindly do this improper integral? It has been a while since I have done it, I am very interested in seeing the solution, and would appreciate a proper refresher. Pun intended. (Nerd)

- Dec 28th 2008, 02:44 AMIsomorphism
- Dec 28th 2008, 03:05 AMProve It
- Dec 28th 2008, 07:13 AMJester
- Dec 28th 2008, 10:24 AMpberardi
Mr. Red,

Would you mind revealing in what class you saw this problem? I am just curious which classes at the graduate level test students on their calculus abilities. Also, was this already set up or was it part of a word problem? Any more information on this would be very interesting.

Thanks. - Dec 28th 2008, 02:27 PMMathstud28
- Dec 28th 2008, 02:45 PMThePerfectHacker
- Dec 28th 2008, 03:48 PMduydaniel
Sorry, I don't know how to write it in proper format.

Here is what I did:

The function should have the following form:

A/(x^2+1) + B/(X^2+4)

then let A = 1 => solve for B:

=> B = -4/(x^2+1)

substitute B back into the function

=> we have something like:

1/(x^2+1) - 4/[(x^2+4)*(x^2+1)]

The second integral need to split up again (Lipssealed). My question is how do you know a proper way to decompose it (as you did)?

Thank you. - Dec 28th 2008, 04:01 PMKrizalid
Note that hence, no partial fractions method involved.

- Dec 29th 2008, 04:04 AMHallsofIvy
That's "partial fractions" and you typically learn it in "Calculus II", a Freshman or Sophomore class (unless you learned calculus in secondary school). I see now that Krizalid did not need partial fractions because he was able to do the fractions easily- he's sharper than I am!

- Dec 29th 2008, 08:15 AMJester
- Dec 29th 2008, 08:36 AMduydaniel