Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/19

1. SECTION

   PAGE

2. 162.

   Normal line to a surface ................................................................................................................................................................................................................................................................................................................................................................................................

   266

3. 163.

   Another form of the equations of the tangent line to a skew curve ................................................................................................................................................................................................................................................................................................................................................................................................

   268

4. 164.

   Another form of the equation of the normal plane to a skew curve ................................................................................................................................................................................................................................................................................................................................................................................................

   269

5.  

   CHAPTER XXI
   CURVES FOR REFERENCE

    

   ---

    

   INTEGRAL CALCULUS

    

   CHAPTER XXII
   INTEGRATION. RULES FOR INTEGRATING STANDARD ELEMENTARY FORMS

6. 165.

   Integration ................................................................................................................................................................................................................................................................................................................................................................................................

   279

7. 166.

   Constant of integration. Indefinite integral ................................................................................................................................................................................................................................................................................................................................................................................................

   281

8. 167.

   Rules for integrating standard elementary forms ................................................................................................................................................................................................................................................................................................................................................................................................

   282

9. 168.

   Trigonometric differentials ................................................................................................................................................................................................................................................................................................................................................................................................

   298

10. 169.

    Integration of expressions containing $\scriptstyle {\sqrt {a^{2}-x^{2}}}$ or $\scriptstyle {\sqrt {x^{2}\pm a^{2}}}$ by a trigonometric substitution ................................................................................................................................................................................................................................................................................................................................................................................................

    304

11.  

    CHAPTER XXIII
    CONSTANT OF INTEGRATION

12. 170.

    Determination of the constant of integration by means of initial conditions ................................................................................................................................................................................................................................................................................................................................................................................................

    307

13. 171.

    Geometrical signification of the constant of integration ................................................................................................................................................................................................................................................................................................................................................................................................

    307

14. 172.

    Physical signification of the constant of integration ................................................................................................................................................................................................................................................................................................................................................................................................

    309

15.  

    CHAPTER XXIV
    THE DEFINITE INTEGRAL

16. 173.

    Differential of an area ................................................................................................................................................................................................................................................................................................................................................................................................

    314

17. 174.

    The definite integral ................................................................................................................................................................................................................................................................................................................................................................................................

    314

18. 175.

    Calculation of a definite integral ................................................................................................................................................................................................................................................................................................................................................................................................

    316

19. 176.

    Calculation of areas ................................................................................................................................................................................................................................................................................................................................................................................................

    318

20. 177.

    Geometrical representation of an integral ................................................................................................................................................................................................................................................................................................................................................................................................

    319

21. 178.

    Mean value of $\scriptstyle {\phi (x)}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    320

22. 179.

    Interchange of limits ................................................................................................................................................................................................................................................................................................................................................................................................

    320

23. 180.

    Decomposition of the interval ................................................................................................................................................................................................................................................................................................................................................................................................

    321

24. 181.

    The definite integral a function of its limits ................................................................................................................................................................................................................................................................................................................................................................................................

    321

25. 182.

    Infinite limits ................................................................................................................................................................................................................................................................................................................................................................................................

    321

26. 183.

    When $\scriptstyle {y=\phi (x)}$ is discontinuous ................................................................................................................................................................................................................................................................................................................................................................................................

    322