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Math Help - def integral with substitution

  1. #1
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    def integral with substitution

    Suppose
    Evaluate the following

    (b)

    Im still feeling a little lost...I'm not sure on when to change the limits, and if du= -dt do i inverse the u? Thanks for all the help!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by gabet16941 View Post
    Suppose
    Evaluate the following

    (b)

    Im still feeling a little lost...I'm not sure on when to change the limits, and if du= -dt do i inverse the u? Thanks for all the help!
    Let u = 6 - t

    \Rightarrow du = -dt \implies -du = dt

    change the limits:

    t = 6 \implies u = 0
    t = 0 \implies u = 6

    so our integral becomes:

    - \int_6^0 g(u)~du = \int_0^6 g(u)~du = 6
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