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Calculus

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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 -

    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 -

    I typed the the answer correctly. At x=2, 65.888-50.461, which is equal to 15.427. So, 15.427-.481= 14.946. Thanks for the help!

  • Calculus -

    yes, it was me who typed the 18 wrong. duh. Anyway, I'm glad that helped.

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