Results 1 to 5 of 5

Math Help - Intro to Integrals

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    10

    Intro to Integrals

    Hi,
    I'm stressing out because I've been on this problem for hours and I'm still getting nowhere.

    The question asks:
    """
    Let R denote the region that lies below the graph of f(x)=2+4x^2 on the interval [-1, 2].

    Estimate the area of R using six approximating rectangles of the same width and
    (a) left endpoints,
    (b) right endpoints
    """

    my prof doesn't really have notes on what to do and I'm really confused since it wants an estimate, and not an exact answer...

    For (a), since the area of one block is:
    (3/n)(2+4(i(3/n))^2)
    but I'm not even sure if that's right...

    Please help me! Student in distress!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,832
    Thanks
    1602
    Quote Originally Posted by alleysan View Post
    Hi,
    I'm stressing out because I've been on this problem for hours and I'm still getting nowhere.

    The question asks:
    """
    Let R denote the region that lies below the graph of f(x)=2+4x^2 on the interval [-1, 2].

    Estimate the area of R using six approximating rectangles of the same width and
    (a) left endpoints,
    (b) right endpoints
    """

    my prof doesn't really have notes on what to do and I'm really confused since it wants an estimate, and not an exact answer...

    For (a), since the area of one block is:
    (3/n)(2+4(i(3/n))^2)
    but I'm not even sure if that's right...

    Please help me! Student in distress!
    It helps if you draw the graph and the rectangles, to give you a picture of what is happening...

    If the region is [-1, 2], this is a distance of 3 units.

    Since you need 6 subintervals, that means that each will be \frac{1}{2} unit. This is going to be the length of each rectangle.

    How do you know the width? You determine the x co-ordinate and its corresponding y. The y co-ordinate represents the width.


    So in your case:

    y = 2 + 4x^2.

    If you are using the left-hand endpoints, then the first x co-ordinate will be -1. So your y co-ordinate is 2 + 4(-1)^2 = 6.

    So A_1 = L\times W

     = \frac{1}{2}\times 6

     = 3\,\textrm{units}^2.


    The second rectangle will be \frac{1}{2} a unit more on the x axis.

    So x = -\frac{1}{2} and y = 2 + 4\left(-\frac{1}{2}\right)^2 = 3.

    So A_2 = L \times W

     = \frac{1}{2}\times 3

     = \frac{3}{2}\,\textrm{units}^2.


    The next rectangle will be at x = 0 and y = 2 + 0^2 = 2.

    So A_3 = L \times W

     = \frac{1}{2} \times 2

     = 1\,\textrm{unit}^2.


    Once you have all the areas you need, you add them up.

    For the right-hand estimate, you start at the right-hand endpoint and go to the left \frac{1}{2} a unit each time.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    10
    Ah crap,

    I overcomplicated it.

    Thought I was supposed to use something the prof taught us.


    Thank you for explaining everything very well!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,832
    Thanks
    1602
    Other methods that give approximations to the area under the curve (and in many cases, better approximations) are the midpoint rule and the trapezoidal rule.

    Rectangle method - Wikipedia, the free encyclopedia

    Trapezoidal rule - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2009
    Posts
    10
    Oh wow, thanks for the links!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Intro to Accounting help
    Posted in the Business Math Forum
    Replies: 2
    Last Post: August 31st 2011, 07:50 PM
  2. intro analysis help
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 7th 2009, 05:39 PM
  3. Intro to Analysis
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 7th 2009, 05:54 AM
  4. Intro to Derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 7th 2008, 06:54 PM
  5. Intro Calc HW
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 3rd 2008, 05:24 AM

Search Tags


/mathhelpforum @mathhelpforum