This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 11 also. They can represent certain solids like cones and
spheres with very compact equations. This will make finding the limits much easier with these solids than using
rectangular coordinates. But we do have an extra factor in our integrand that emerges with spherical. This is akin to the
variable r that popped up when we used polar.
First let’s look at the representation of a point with spherical: Solids represented with spherical coordinates: Spherical to Rectangular: Sphere:
Now we will derive the extra factor that appears in the integrand while using spherical coordinates. In section 13.8 we
will re-derive this factor approaching it from a change of variables perspective.
We will first look at the projection of the solid in the xy-plane and represent the area of that projection with a double
This will be just like what we did for polar except instead of r we are now using . Thus Area = Now for volume we need the height. Remember for cylindrical how we...
View Full Document