Lesson 11 of 18Article18 min
Applications of Integrals: Area, Volume & Accumulation
Between y = f(x) and y = g(x) from x=a to x=b, area = ∫ₐᵇ |f−g| dx. Split where the upper curve changes.
Area between curves
Between y = f(x) and y = g(x) from x=a to x=b, area = ∫ₐᵇ |f−g| dx. Split where the upper curve changes.
Volumes by slicing
Disk/washer: rotate a region about an axis; cross-sections are disks or washers. Volume is ∫ π(R² − r²) dx (or dy).
- Identify the axis of rotation and variable of integration.
- Express outer/inner radius as functions of that variable.
- Set limits from the interval of the solid.