http://web.mit.edu/abhinavk/www/inte...e/qual2011.pdf
Nothing terribly exciting. But you're only given 20 minutes to answer 25 questions. Feel free to post a solution or two.
Moderator edit: Moved to this subforum from Calculus (because I think the intent of the post is to provide a challenge ....?)
Here's another way to do 4:
----------
Here's 8:
----------
Here's another way for 12 (note 1/cos x = sec x):
Rmk: it involves some algebra, but TCM's solution is the same as mine.
----------
16:
----------
20:
----------
21:
by geometry (this is the area of the upper half-circle of radius 3).
P.S. What on earth is the philosophy of that test?
Fernando Revilla
perhaps this is one of the most boring integral bee, i remember old ones had much interesting problems.
15) you don't want to use product to sum formulae, we just put and that gives the same integral with a minus sign, since both are equal, then is obvious that the integral equals zero.
Having read the file of this test , i wonder whether it is possible to design a similar test representing this forum ( or we can just call it ' 2011 MHF Integration Bee Qualifying Test ' ) . In the test , I suggest proposing more difficult problems and to be more meaningful , I think all of the problems should be designed by our members ( it may be a difficult job ... or we can modify the old problems ) . All members are welcome to post their own problems , their problems will be put into the shortlist and finally 6 of them will be chosen for the test .