Results 1 to 4 of 4

Math Help - find an upper/lower bound for the integral

  1. #1
    Newbie
    Joined
    Aug 2006
    Posts
    13

    find an upper/lower bound for the integral

    Hello, am a complete novice attempting an on-line course, can you show me how to work this problem? Thanks for your time.

    Find an upper and lower bound for the integral \int_{0}^{1}\frac{1}{x+2}dx using the comparison properties of integrals.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by FLTR
    Hello, am a complete novice attempting an on-line course, can you show me how to work this problem? Thanks for your time.

    Find an upper and lower bound for the integral \int_{0}^{1}\frac{1}{x+2}dx using the comparison properties of integrals.
    Maybe this will help, for x>0
    0<\frac{1}{x+2}<\frac{1}{x}
    Then,
    0<\int_0^1 \frac{dx}{x+2} < \int_{0^+}^1 \frac{dx}{x}=\ln x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, FLTR!

    Find an upper and lower bound for the integral \int_{0}^{1}\frac{1}{x+2}dx
    using the comparison properties of integrals.

    Since 0 \leq x \leq 1:\;\;2\:\leq \;x+2\:\leq \:3\quad\Rightarrow\quad \frac{1}{3} \,\leq \,\frac{1}{x+2} \,\leq \,\frac{1}{2}

    Hence: . \int^1_0\!\frac{1}{3}\,dx \;\leq \;\int^1_0\!\!\frac{dx}{x+2} \; \leq \; \int^1_0\!\frac{1}{2}\,dx

    Therefore: . \frac{1}{3} \;\leq \;\int^1_0\!\!\frac{dx}{x+2} \;\leq \;\frac{1}{2}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2006
    Posts
    13
    Thanks for the examples. I should be able to work the remaining exercises, at least on this type of problem!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find lower bound of integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 19th 2011, 04:14 PM
  2. Replies: 0
    Last Post: February 19th 2010, 01:06 AM
  3. Upper bound/Lower bound?
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: September 13th 2009, 10:48 AM
  4. Replies: 1
    Last Post: April 2nd 2008, 10:54 PM
  5. least upper bound and greatest lower bound
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 22nd 2007, 09:59 AM

Search Tags


/mathhelpforum @mathhelpforum