1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Volume of a Solid- 3D Calculus

  1. Apr 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the given solid.
    Bounded by the planes
    z = x, y = x, x + y = 5 and z = 0

    2. Relevant equations
    V = [PLAIN]http://www.webassign.net/wastatic/wacache6cdd60ea0045eb7a6ec44c54d29ed402/watex/img/integral.gif[PLAIN]http://www.webassign.net/wastatic/wacache6cdd60ea0045eb7a6ec44c54d29ed402/watex/img/integral.giff(x,y) [Broken] dA
    For a type I integral: dA=dy*dx
    and the domain is: a<x<b, g1(x)<y<g2(x)

    For a type II integral: dA=dx*dy
    and the domain is: c<y<d, h1(y)<x<h2(y)

    3. The attempt at a solution

    I chose to evaluate this integral by making region D as a type I integral, therefore my domain is as follows:
    0<x<5/2 & x<y<5-x
    My f(x,y)=x

    Is it possible to do this as a type II integral? That way my limits would look a lot nicer, but I don't know what my h1(y) and h2(y) functions would be.

    Attached Files:

    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. May 1, 2016 #2

    Buzz Bloom

    User Avatar
    Gold Member

    Hi fridakahlo:

    I think that when you calculate a volume by integration you need an integral of the form
    V = ∫∫∫ f(x,y,z) dV = = ∫∫∫ f(x,y,z) dx dy dz

    Hope this helps.

  4. May 1, 2016 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No, a volume integral would just be ∫∫∫dxdydz, no need for a function. But in this case fridakahlo is effectively assuming the z integral has been done, leaving either ∫∫fdxdy or ∫∫dydx.

    @fridakahlo , yes you can do the x integral before y, but you would need to split the outermost integral into two ranges, y<2.5 and y>2.5.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted