Results 1 to 2 of 2

Thread: Prove that a function is integrable

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    27

    Prove that a function is integrable

    Hey all,
    I am supposed to solve problems like these. If someone can help me with this, I should be able to figure out the rest. I just dont know which theorem to use out of all the given ones.

    PS: Its the first time I'm using latex to submit a question, I was able to figure out how to adjust the image sizes, but not the spaces between words. Apologies.

    $\displaystyle
    Prove that \int_0^b x^3 dx = b^4/4, by
    considering
    partitions
    into
    n
    equal $
    $\displaystyle subintervals, using the formula \sum_{i=1}^n i^3 = n^4/4 + n^3/2 + n^2/4
    $
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,771
    Thanks
    3028
    Well, what have you tried to do yourself?

    If you divide the interval from 0 to b into n equal length subintervals, what is the length of each subinterval? If you take $\displaystyle x_i$ to be the right hand endpoint of each subinterval, what is $\displaystyle x_i$ in terms of i? Then $\displaystyle (x_i)^3$ is the height of each rectangle what the length of the subinterval is the base. The area of each rectangle is the product of those two. Find the entire area by summing those. With any luck, you will get a sum that looks like $\displaystyle \sum i^3$, perhaps multiplied by other numbers.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Prove that a function is Riemann integrable?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: Aug 29th 2010, 10:57 AM
  2. Prove that this function is integrable
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Dec 22nd 2009, 10:06 AM
  3. Replies: 0
    Last Post: Dec 1st 2008, 06:43 PM
  4. Prove a function is integrable
    Posted in the Calculus Forum
    Replies: 12
    Last Post: Feb 12th 2007, 09:51 AM
  5. To prove a function is integrable (or not)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jan 26th 2007, 03:15 PM

Search Tags


/mathhelpforum @mathhelpforum