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
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