Results 1 to 2 of 2

Math Help - Two questions involving integration

  1. #1
    Member
    Joined
    Mar 2008
    Posts
    78

    Two questions involving integration




    I cannot use integration by parts or numerical methods since that has not been introduced in the course. I know if I find a lower Riemann sum that equals the term on the left and an upper Riemann sum that equals the term on the right, that will work. But if that is the correct approach, then I'm not sure how to pick them.

    edit: sorry just one question, I solved the other one but forgot to change the title

    edit 2: actually what if you choose a partition P with two points {1, 2}.

    Then 1/2e(e-1) < e < integral < e^2/2 < e(e-1)

    since e is the lower Riemann sum for P and e^2/2 is the upper Riemann sum for P

    is this correct?
    Last edited by paulrb; April 12th 2011 at 05:51 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293
    Note that in the region \displaystyle -1 \leq x \leq 2,

    \displaystyle \frac{e^x}{2} \leq \frac{e^x}{x} \leq e^x.

    So \displaystyle \int_1^2{\frac{e^x}{2}\,dx} \leq \int_1^2{\frac{e^x}{x}\,dx} \leq \int_1^2{e^x\,dx}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Questions Involving Rings
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 4th 2009, 01:37 AM
  2. Questions Involving Cosets
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 14th 2009, 07:52 PM
  3. A Few Questions Involving Subgroups
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: February 12th 2009, 09:39 PM
  4. Questions involving continuity
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 18th 2008, 05:07 PM
  5. A few questions involving limits
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2008, 02:27 AM

/mathhelpforum @mathhelpforum