Thread: What Integration Technique? View Single Post
2008-04-28, 02:55   #11
davieddy

"Lucan"
Dec 2006
England

6,451 Posts

Quote:
 Originally Posted by frmky As hinted above, shift the origin by 3 to get a symmetric integral over -1 to 1. Call this integral 1. Then replace x by -x (and of course dx by -dx) and see what you get as an equivalent integral. Call this integral 2. Now add integral 1 and integral 2 to get an integral that is easier to do. Call this integral 3. Now, since integral 1 and 2 are equal, they are each 1/2 of integral 3.
If "technique" is required, I would show that integrating
f(x) from 2 to 3 was the same as integrating f(3-y) from y=0 to 1.
More trivially, integrating f(x) from 3 to 4 is the same as
integrating f(3+y) from y=0 to 1.

Summing these I would then conclude that the answer was
the integral of (f(3+y) + f(3-y)) from y=0 to 1.

Last fiddled with by davieddy on 2008-04-28 at 03:34