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Kuma
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Homework Statement
Here is the question given:
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?
Kuma said:Homework Statement
Here is the question given:
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?
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.
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.
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.
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.
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.