Posted by Anonymous on Wednesday, June 4, 2008 at 9:27pm.
integral 1 to 500 (13^x  11^x) + integral 2 to 500 (11^x  13^x) dx =
(answer: 14.946)
I tried typing the integrals in the graphing calculator to get the answer, but it says overflow. Any help on solving this? Thanks!

Calculus  drwls, Wednesday, June 4, 2008 at 9:53pm
Note that the integrand of #2, is inues that of #1, so that the two integrals cancel over the 2 to 50 range, just the integral of (13^x  11^x) from 1 to 2.
Recognizing that the 2 to 500 part of the integrals, which are extremely large numbers, cancel out should help you avoid the overflow problem.
The answer is integral 1 to 2
(13^x  11^x) dx
The integral of a^x is a^x/log a, so
The indefinite integral is
13^x/log 13  11^x/log 11
At x = 2, this is 65.888  50.461 = 18.427
At x = 1, is it 5.068  4.587 = 0.481
Take the difference of those two numbers for the final answer. it is 17.946.., not 14.946
I think you typed it wrong. 
Calculus  Anonymous, Wednesday, June 4, 2008 at 10:31pm
I typed the the answer correctly. At x=2, 65.88850.461, which is equal to 15.427. So, 15.427.481= 14.946. Thanks for the help!

Calculus  drwls, Wednesday, June 4, 2008 at 10:40pm
yes, it was me who typed the 18 wrong. duh. Anyway, I'm glad that helped.