Integral Calculus
Calculus Contents E
      The definite integral
      The area between the graph of a function and the x-axis over a closed interval
         The upper sum and the lower sum
      The definition of the definite integral
         Riemann sum
      Calculating a definite integral from the definition
         Calculating a definite integral from the definition examples
      Physical applications to the definite integral
         Describing motion of objects using velocity - time graphs
      Evaluating the area under the graph of a function using the definition of the definite integral, examples
      The definite and indefinite integrals
      The area between the graph of a function and the x-axis over a closed interval
         Geometric interpretation of the definite integral
      Properties of the definite integral
         The definite integral over interval of zero length
         Reverse order of integration
         The constant multiple rule
         The integral of the sum or difference of two functions
         Internal addition of the definite integral
         The definite integral of an odd function
         The definite integral of an even function
         The definite integral of a nonnegative and nonpositive functions
         Relationship of the definite integrals of two functions over the same interval of integration
         Absolute integrability
         The mean value theorem
         The average value of a function over the given interval
      The indefinite integral
         Integration - inverse of differentiation
         Constant of integration, the arbitrary constant term in the expression of the indefinite integral
         Evaluating the indefinite integral example
      The fundamental theorem of calculus
         The fundamental theorem of differential calculus
      Evaluating definite integrals using indefinite integrals
         The fundamental theorem of integral calculus
         Evaluating the definite integral examples
    a)  The indefinite integral
      Basic rules of integration
         Table of indefinite integrals
      The indefinite integral applications
         Kinetic equation of free fall
         Exponential growth and decay (increase and decrease)
      Evaluation of indefinite integrals using some basic integration rules and formulas, examples
    b)  The indefinite integral methods for solutions
      Substitution rule
         Evaluating the indefinite integrals using substitution rule examples
         Evaluating the indefinite integrals using substitution rule solutions
      Integration by parts rule
         Evaluating the indefinite integrals using the integration by parts formula examples
         Evaluating the indefinite integrals using the integration by parts formula solutions
 
 
 
 
 
 
Copyright 2004 - 2020, Nabla Ltd.  All rights reserved.