Triple integral spherical coordinates.

In summary, the question is asking how to find restrictions on the two angles, theta and phi, given a value for p. The suggested approach is to draw a picture and consider the usual range for these angles on a sphere.
  • #1
Kuma
134
0

Homework Statement



Here is the question given:

jZVUZ.png



Homework Equations





The Attempt at a Solution



So i set p as x^2 + y^2 + z^2

so p lies in between b and a.

But how do i find the restrictions on the two angles, theta and phi?
 
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  • #2
Kuma said:

Homework Statement



Here is the question given:

jZVUZ.png



Homework Equations





The Attempt at a Solution



So i set p as x^2 + y^2 + z^2

so p lies in between b and a.

But how do i find the restrictions on the two angles, theta and phi?

Hopefully you mean [itex]\rho=\sqrt{x^2+y^2+z^2}[/itex]. Draw a picture. What do [itex]\phi\hbox{ and }\theta[/itex] usually range through for spheres?
 

1. What are spherical coordinates?

Spherical coordinates are a system of coordinates used to specify the location of a point in three-dimensional space. They use three parameters: radius, inclination, and azimuth. The radius measures the distance from the origin to the point, the inclination measures the angle from the positive z-axis to the point, and the azimuth measures the angle from the positive x-axis to the projection of the point onto the xy-plane.

2. How do spherical coordinates differ from Cartesian coordinates?

Spherical coordinates differ from Cartesian coordinates in that they use a radius, inclination, and azimuth to specify a point in 3D space, whereas Cartesian coordinates use x, y, and z coordinates. Spherical coordinates are often more useful for describing points on a sphere or in situations with spherical symmetry.

3. What is a triple integral in spherical coordinates used for?

A triple integral in spherical coordinates is used to find the volume of a solid bounded by a curved surface. It is also used in other applications such as calculating the moment of inertia of a solid and solving certain differential equations.

4. How do you convert a triple integral in Cartesian coordinates to spherical coordinates?

To convert a triple integral from Cartesian coordinates to spherical coordinates, you first need to express the limits of integration in terms of the spherical coordinates parameters. Then, you substitute the Cartesian coordinates with the corresponding spherical coordinates expressions and adjust the integrand accordingly. Finally, you evaluate the integral using the appropriate spherical coordinates formula.

5. What are some common applications of triple integrals in spherical coordinates?

Triple integrals in spherical coordinates are commonly used in physics, engineering, and mathematics. They are particularly useful in situations with spherical symmetry, such as modeling gravitational or electric fields, calculating the volume of a spherical object, or finding the center of mass of a solid with a spherical shape.

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