Applications of the Integral
Though the pratical problems are complex and full of diversity, we can generalize them into a few common types. To calculate by ourselves, we have the applications below.
Find the Area
From the first fundamental theorem of calculs we know that the integration is actually the process of finding an area between a given curve and the x axis.
Find the Volumn
The core idea of finding the volumn is to find the sum of many small slabs. For solids with regular shapes, is to find the function which depict the change of the shape and then do the integration.
We mainly talk about solids of revolution here.
Method of Disks
- Find the axis of revolution.
- Imagine to cut the solid into many disks along the axix.
- Find the function of the edge of the revolution.
- Do the intergation.