Results 1 to 3 of 3

Thread: How To Find the Definite Integral Of This:

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    123

    How To Find the Definite Integral Of This:

    Thanks. This is useful.
    Last edited by AlphaRock; Jan 13th 2010 at 01:13 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,002
    Thanks
    1
    It is given as Riemann sum.

    The subintervals are $\displaystyle \frac{6-0}{n}=\frac{6}{n}$

    The integral is:

    $\displaystyle \int_{0}^{6}e^{4+x}dx$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    339
    Thanks
    46
    On top of what the last poster offered, this is what I wrote up (and forgot to send a long time ago because I got enormously side-tracked):


    $\displaystyle
    \lim_{n\to\infty} \sum_{i=1}^n e^{4+\frac{6i}{n}} \cdot \frac{6}{n} = $ $\displaystyle

    \lim_{n\to\infty} \sum_{i=1}^n e^4\cdot e^{\frac{6i}{n}}\cdot\frac{6}{n} = $ $\displaystyle

    \lim_{n\to\infty} e^4\cdot \sum_{i=1}^n e^{\frac{6i}{n}}\cdot\frac{6}{n} = $ $\displaystyle

    e^4 \cdot \lim_{n\to\infty}\sum_{i=1}^n e^{\frac{6i}{n}}\cdot\frac{6}{n} = $ $\displaystyle

    e^4 \cdot \lim_{n\to\infty}\sum_{i=1}^n e^{(\frac{6}{n})i}\cdot\frac{6}{n} = $ $\displaystyle

    e^4 \cdot \lim_{n\to\infty}\sum_{i=1}^n \bigg(e^{(\frac{6}{n})i}\bigg)\bigg(\frac{6}{n}\bi gg) $


    Let $\displaystyle x_i^* $ be the right-hand endpoint of the $\displaystyle i^{\text{th}} $ subinterval; i.e.,

    $\displaystyle x_i^* = \frac{6i}{n} $, for $\displaystyle i= 1,2,...,n $

    Thus,

    $\displaystyle \Delta x_i = \frac{6}{n} $ , $\displaystyle a =x_0 = \frac{6 \cdot 0}{n}=0$ , and $\displaystyle b =x_1= \frac{6 \cdot n}{n}=6 $


    And we have:

    $\displaystyle
    \lim_{n\to\infty} \sum_{i=1}^n e^{4+\frac{6i}{n}} \cdot \frac{6}{n} =
    e^4 \cdot \int_{0}^6 = e^x dx = \int_{0}^6 = e^4 \cdot e^x dx = \int_{0}^6 = e^{x+4} dx
    $
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Can we find THIS definite integral?
    Posted in the Calculus Forum
    Replies: 12
    Last Post: Mar 1st 2011, 05:52 AM
  2. Find the Definite Integral
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Sep 24th 2010, 07:41 PM
  3. How to find the definite integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 6th 2010, 03:55 PM
  4. Find the value of Definite Integral
    Posted in the Calculus Forum
    Replies: 14
    Last Post: Dec 28th 2009, 10:17 PM
  5. Find the definite integral using substitution
    Posted in the Calculus Forum
    Replies: 12
    Last Post: Sep 25th 2009, 12:25 AM

Search Tags


/mathhelpforum @mathhelpforum