Area and volume calculus

Area and volume calculus

by Souad Ayadi -

1/ What is the main difference between a surface area and a volume?

2/     Why do we need double integrals for computing areas and triple integrals for computing volumes?

3/  In your own words, explain what the element dA or dV represents in an integral.

4/ How do we compute the volume of a solid in cylindrical and spherical coordinates?

Area and volume calculus

by SMAIL ISLAM -
1. Surface area measures 2D covering; volume measures 3D space.


2. Areas are 2D → double integrals; volumes are 3D → triple integrals.


3. dA and dV are tiny pieces of area or volume used to add up the total.


4. Change to cylindrical or spherical coordinates, use the proper formula, and integrate.