ehild said:
ok so ∅ goes from 0 to 2pi as it is some sort of sphere/ elipse. correct?ehild said:
ahhh so θ goes from 0 to piehild said:
r goes from 0 to 2ehild said:
Yes.uzman1243 said:
Spherical coordinates are a system of coordinates used to describe points in three-dimensional space. They consist of a radial distance from the origin, an azimuth angle measured from a reference direction, and an elevation angle measured from the reference plane.
Spherical coordinates are useful when working with three-dimensional problems that involve spherical symmetry. They are also commonly used in physics and engineering for describing the position and movement of objects in three-dimensional space.
To convert from spherical coordinates (r, θ, φ) to Cartesian coordinates (x, y, z), use the following equations:
x = r sinφ cosθ
y = r sinφ sinθ
z = r cosφ
where r is the radial distance, θ is the azimuth angle, and φ is the elevation angle.
The limits of an integral in spherical coordinates are determined by the shape and boundaries of the region being integrated. To find the limits, you must first determine the range of the radial distance, azimuth angle, and elevation angle within the region. Then, set up the integral using these limits and integrate according to the appropriate formula.
Some common mistakes when finding limits of integrals in spherical coordinates include:
- Forgetting to convert the limits to the appropriate units (e.g. converting radians to degrees)
- Using the wrong integration formula for the given region
- Not considering the symmetry of the region and including unnecessary limits
- Confusing the order of the limits, which can result in incorrect answers.
