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(3y) 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(3y)) from y=0 to 1.