Multiple Integrals Examples
- Colin Desmarais
- Calculus, Cone, Definite Integral, Solids or 3D Shapes, Sphere, Surface, Volume
Change of variables in triple Integrals
The task is to set up the integral needed to calculate a volume between two surfaces. Below is the image of a cone and a sphere, with the given equations
We want to find the volume between the surfaces (above the cone and below the sphere). To do this, we change to spherical coordinates.
Below is a volume defined using spherical coordinates. Change the maximum values of , , and to get a volume that corresponds to the volume between the cone and the sphere above.