Integral Calculus
Calculus Contents F
      The indefinite integrals
    c)  Types of the indefinite integrals
      The indefinite integrals containing quadratic polynomial (trinomial)
         The indefinite integrals containing quadratic polynomial examples
      Recursion formulas - use of integration by parts formula
         Recursion formulas - use of integration by parts formula examples
      Integrating rational functions
         Use of the partial fraction decomposition to integrate a proper rational function
         Use of the partial fraction decomposition to integrate a proper rational function examples
         The Ostrogradsky method of the integration of a proper rational functions
         The Ostrogradsky method of the integration of a proper rational functions examples
      Integrating irrational functions
         Integration of irrational functions examples
         Integrals of the form
 
         Euler's substitutions
         Integrating irrational functions using Euler's substitutions examples
      Binomial integral
         Solving binomial integrals examples
      Trigonometric integrals
         Trigonometric integrals of the form sinm x, cosn x dx
         Trigonometric integrals of the form
          sin (m x) sin (n x) dx,    sin (m x) cos (n x) dx,    cos (m x) cos (n x) dx.
         Integrals of the rational functions containing sine and cosine,   R (sin x, cos x) dx
         Use of trigonometric identities and substitutions to solve trigonometric integrals
      Integrals of the hyperbolic functions
      Substitution and definite integration
         Substitution and definite integration examples
      Integrations by parts and the definite integral
      The improper integrals
         The improper integral definition
         The improper integrals examples
      Differentiation and integration of infinite series
         Differentiation and integration of infinite series examples
      Differentiation and integration of power series
     Applications of the definite integral
      The area of a region in the plane
         The area between the graph of a curve and the coordinate axis
         The area between the graph of a curve and the coordinate axis examples
         The area bounded by a parametric curve
         The area of the sector of a curve in polar coordinates
         The area of the sector of a curve given in Cartesian (or rectangular) coordinates
         The area of the sector of a parametric curve
      The area between two curves
         The area between two curves examples
      Length of plane curve, arc length
         Arc length of a parametric curve
         Arc length of a curve in polar coordinates
      The volume of a solid of revolution
         The volume of a sphere
         The volume of a spherical segment
         The volume of a cone
      The surface area of a solid of revolution
         The lateral surface area of a cone
         The surface area of a spherical cap
         The surface area of an ellipsoid
 
 
 
 
 
 
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