Explore BrainMass

Explore BrainMass

    Integration: Standard Partition, Integrable over a Range

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Questions on integration, see attachment.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:13 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integration-standard-partition-integrable-over-range-8243

    Attachments

    Solution Preview

    Please see the attached file for the full solution.

    Thanks for using BrainMass.

    1. Proof. Since 0 x /2, 0 Sin(x) 1.
    So 2 2+Sin(x) 3. Thus,

    (1+x) (1+
    So,

    So,

    *( /2) (1+ /2)* ( /2)= (2+ )* ( /4)
    as desired.

    2. Solution. By the Stirling formula we have,

    n!~
    where ~ is used to indicate the ratio of both sides goes to 1 as n tends to infinity.
    By the definition of = and the Stirling formula, we have (as n-> )

    ~ / ...

    Solution Summary

    The integration for standard partition and integrable over a range are determined.

    $2.19

    ADVERTISEMENT