0 less than or equal to theta that is less than or equal to pie/3© BrainMass Inc. brainmass.com October 24, 2018, 11:39 pm ad1c9bdddf
The expert sketches the region in the plane consisting of points whose polar coordinates satisfy the given conditions.
Vectors Calculas & Applications
See the attached file.
1. Evaluate the integral:
** see the attachment for the full equation **
Where D is the domain given by: 1 ≤ x^2 + y^2 ≤ 4 and y ≥ 0.
2. (i) Find the area of the region enclosed by the ellipse (x^2/a^2) + (y^2/b^2) = 1
(ii) Find the area of the region enclosed by the parabola y = x^2 and the line y= x + 2.
Sketch the region.
3. Calculate the mass of a spherical bead of radius 3, centered at the origin, if the density of the material it is made of, is given by the function :
4. Evaluate the moment of inertia of a cylinder of radius R and height L about its axis of symmetry, if the density varies with distance from the axis as p = a(x^2 + y^2). Express the result in terms of the cylinder mass.
5. Calculate the volume of the ellipsoid
(x^2/a^2) + (y^2/b^2) + (z^2/c^2) ≤ 1.