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Old 2008-04-28, 02:55   #11
davieddy
 
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"Lucan"
Dec 2006
England

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Quote:
Originally Posted by frmky View Post
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
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