CONTENTS ix 

 CHAPTER XII 



PAGE 



Integration of Trigonometrical Functions . . . 178 



CHAPTER XIII 



Integration by Parts . 188 



CHAPTER XIV 



The Meaning of an Integral . . . . .192 



The Definite Integral 193 



Areas 194 



Volumes of Surfaces of Revolution 199 



CHAPTER XV 



TheCentroid 208 



CHAPTER XVI 



Moment of Inertia and the Principal Axes of Inertia . . 222 



Momenta! Ellipse 227 



Moment of Inertia of Areas ....... 229 



Moment of Inertia of Solids . 239 



CHAPTER XVII 



Trapezoidal and Mid-ordinate Rules ..... 247 



Simpson's Rule . 248 



Prismoidal Rule . 252 



The Derived Figures 258 



CHAPTER XVIII 



Lengths of Curves 268 



Areas of Surfaces of Revolution 272 



Polar Co-ordinates 279 



