Find the mass of the tetrahedron with vertices (0,0,0), (0,1,0), (3,0,0), and (0,1,4) with density f(x,y)= xy using iterated integral

Related BrainMass Solutions

• Stroke's Theorem and Direct Evaluation

  We know that for every point P(x,y,z) on S, its direction vector is (x,y,z), so we have = = = (b) Find the flux of the vector field F(x,y,z) = (y-x)i + (x+y)j + y k across the side of the triangle with vertices at (1,0,0), (0,1,0) and (

• center of mass coordinate for each coordinate

  We need to integrate the density of our object (constant, 1) over the volume of our object. If we weight this integral with a position variable (x,y or z) then we get the center of mass coordinate for each coordinate. See attached for details.

• Stokes and Gauss' Theorem

  74243 Stokes and Gauss' Theorem 1. A vector field v(x, y, z) is given by the formula v(x, y, z) = xyˆx − yˆ2y. Consider a square path in the xy plane which starts at (0,0,0) and moves along the corners (1,0,0), (1,1,0) and (0,1,0).

• Tetrahedron length and angles

  218771 Vectors Consider a regular tetrahedron with vertices: (0,0,0) , (k,k,0) , (k,0,k) , and (0,k,k) a) sketch the graph of the tetrahedron b) find the length of each edge c) find the angle between any two edges d) Find the angle between

• Multiple Intergration, Area, Center of Mass, Centroid and Jacobian

  d) Set up the integral to find the moment of the solid in part b) about the xy-plane. e) Set up the integral for finding the surface area of f(x, y) = ?x^2 + 4x above R. 1) Find the mass of the solid from part c) if d(x,y,z) = 2x.

• Work, Scalar Projection and Diagonal of a Cube

  Projecting the first vector onto the second gives: Distance= Consider the cube with vertices (0,0,0),(0,0,1),(1,0,0),(0,1,0),(1,1,1), (1,1,0),(1,0,1),(0,1,1). The diagonal has length . Consider the diagonal from (0,0,0) to (1,1,1).

• Iterated Integrals Evaluated

  Set up the integral as an iterated integral in which the x integration is done first, and as an iterated integral in which the y integration is done first, and then evaluate the integral using the latter setup.

• multivariable calculus

  (  ^n_r means that n is on the top of the  and r is on the bottom) Evaluate the iterated integral :  ^1_0  ^(x^2)_0 xy dy dx : is the integral symbol f = integral sign
  
  f^1_

• application of triple and double integrals

  Find the volume of the given solid 30. Under the surface z = x^2y and above triangle in the xy-plane with vertices (1, 0), (2, 1), and (4, 0). 32. Bounded by the cylinder x^2 + y^2 and the planes z = 0 and y + z = 3. 34.