Elementary Integral Calculus

Preface; Historical sketch; 1. Definitions and standard forms; 2. Integration by substitution, or changing the subject of integration; 3. Integration by parts; 4. Rational algebraic fractions; 5. Trigonometrical integrals and formulae of reduction; 6. The fundamental 'inversion theorem'. Application of calculus to finding of areas; 7. Further applications to geometry: sectorial areas, volumes of revolution, finding the length of a curve; 8. Application to problem of finding centres of gravity; 9. Further applications to mechanics. Rigid dynamics; 10. Differential equations. A few types; Answers to examples.