PsychonautQQ said:Homework Statement
Computer the integral of f(x,y,z) = x^2+y^2 over the sphere S of radius 4 centered at the origin.
The Attempt at a Solution
so if the parameters for a sphere are in terms of (p,θ,∅)
,
triple integral (p^2((psin∅cosθ)^2+(psin∅sinθ)^2))dpdθd∅)
where the boundaries on dp is 0 to 4, and then dθ and d∅ are both 0 to 2∏
am I on the correct track here?
A "Computing integral over a sphere" refers to the process of calculating the value of an integral over a sphere, which involves finding the area under a curve on the surface of a sphere.
Computing an integral over a sphere is important in many fields of science, such as physics, engineering, and mathematics. It allows for the determination of important quantities, such as the volume, surface area, and mass distribution of a sphere.
There are several methods for computing an integral over a sphere, including the spherical coordinates method, the Monte Carlo method, and the Gauss-Legendre method. Each method has its own advantages and is suitable for different types of integrals.
Computing an integral over a sphere is used in many applications, such as calculating the gravitational potential of a spherical mass distribution, finding the moment of inertia of a solid sphere, and determining the electric field around a charged sphere.
One of the main challenges in computing an integral over a sphere is dealing with the singularity at the center of the sphere. This can be addressed by using appropriate mathematical techniques, such as regularization or singular value decomposition. Another challenge is determining the appropriate method for a given integral, as some methods may be more efficient or accurate for certain types of integrals.