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# Sketch a region with polar coordinates

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Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.

0 less than or equal to theta that is less than or equal to pie/3

https://brainmass.com/math/functional-analysis/sketch-region-polar-coordinates-200757

#### Solution Summary

The expert sketches the region in the plane consisting of points whose polar coordinates satisfy the given conditions.

\$2.19

## 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 :
p(x,y,z)=2|z|

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.

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