Results 1 to 2 of 2

Thread: Integrating a volume

  1. #1
    Junior Member
    Sep 2009

    Integrating a volume

    We just started today and a problem I have is...

    Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown in the figure below. Evaluate the integral exactly. Use your work to answer the questions below.

    What is the approximate volume of the slice with respect to y?

    So I got l/14=(7-y)/7 and then I get 20y deltay is the volume of the slice but it is a circle, where would I put pi into this?

    Thanks for the help,

    Attached Thumbnails Attached Thumbnails Integrating a volume-53286.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    DBA is offline
    May 2009
    The area of the cut is a rectangle A=2x*10
    Radius is 7 so x=7
    V = \int_{a}^{b}A(y)dy

    In your case you have

    V = \int_{a}^{b} 2x * 10 dy = 20 \int_{a}^{b} x dy

    So, you need to write the x in terms of y, since you have dy

    The point (x,y) is on the circel
    $\displaystyle x^{2} + y^{2} = r^{2}$
    $\displaystyle x^{2} + y^{2} = 7^{2}$

    $\displaystyle x = \sqrt {49-y^{2}}$

    V = 20 \int_{0}^{7} \sqrt {49-y^{2}} dy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Nov 18th 2011, 01:08 PM
  2. Replies: 1
    Last Post: May 14th 2010, 04:08 PM
  3. divergence = flux / volume is independant of the limiting volume
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Apr 26th 2010, 07:31 PM
  4. integrating help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 1st 2009, 09:42 AM
  5. Integrating
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 12th 2007, 10:12 PM

Search tags for this page

Search Tags

/mathhelpforum @mathhelpforum