All the chapter exercises, in order of appearance in the book: first the problems on Cavalieri’s principle, then the computation of integrals with the antiderivative and the various techniques (substitution, parts, partial fractions), volumes of revolution, areas between curves and improper integrals.
- Equivalent pyramids via Cavalieri
- Volume of revolution via Cavalieri
- Hemisphere and cylinder via Cavalieri
- Equivalent triangles (Cavalieri 2D)
- Integral using the antiderivative
- Antiderivative through a point
- Integral by substitution
- Integration by parts of the logarithm
- Partial fractions
- Volume of the sphere of radius 5
- Revolution about the y axis with shells
- Exponential improper integral
- Area between a parabola and a line
- Improper integral with a root