Practice question · Select all that apply
Select every quantity that is computed by accumulating infinitesimal pieces, that is, by an integral.
Hints
- Separate the quantities that are totals from the ones that are rates at a point.
- Anything 'instantaneous' is the derivative's business, not the integral's.
Show the answer
- B. The work done by a variable force
- C. The volume of a solid of revolution
- D. The area between two curves
Why
Work, area and volume are all totals assembled from infinitesimal pieces. Instantaneous velocity and the slope of a tangent are values at a single point, which is what derivatives compute, the two operations are inverse, so knowing which question is being asked tells you which tool applies.
Practise Applications of Integration
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