Math 314 Lecture #26 §15.9: Triple Integrals in Spherical Coordinates PDF

Cylindrical and Spherical Coordinates

26-Jan-2017 the yz-plane (where x = 0) and the xz-plane (where y = 0) we consider the region in the first octant under the sphere and above the cone

These three coordinate planes divide space into eight parts called octants. The first octant

https://www3.nd.edu/~zxu2/triple_int16_7.pdf

(and this equation defines the plane); the yz plane is defined by the octant in which all three coordinates are positive is called the first octant.

surface S defined as the level set of f (xy

23-Nov-2010 1 and the sphere x2 + y2 + z2 = 16

surface integral (1) is defined to be this limit. (The surface has to be sphere x2 + y2 + z2 = a2 lying in the first octant (x y

the origin the angle ? the projection of P on the xy-plane makes with the Find a spherical coordinate description of the solid E in the first octant.

Find the volume in the first octant bounded by y2 = 4 ? x and y = 2z. ? The surface is a portion of the sphere of radius 2 centered at the origin ...

Now function g must be evaluated on the surface S. That means sphere x2 + y2 + z2 = a2 in the first octant in the direction away from the origin.