- The geometric area between a curve and the x-axis
- The geometric area between two curves
- The distance and displacement of a moving object, given its velocity
- The volume of a three-dimensional shape with known cross-sections
- The total amount of resources consumed, given the rate at which they are being consumed
- The arc length of a curve
"Integrals are used..."
- [to] break... the whole into many parts … and add... them all together
- [when] the function is curved or irregular
- [to find] the amount of … stuff when all that is known is … the rate of production
- to compile infinite measurements into one analytical expression
- [to find] accumulated change