Integration

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11 videos in this playlist

Integration as Summation
Integration may be introduced as a means of finding areas using summation and limits. This process gives rise to the definite integral of a function.
Integration as the Reverse of Differentiation
Integration can be seen as differentiation in reverse; that is we start with a given function f(x), and ask which functions, F(x), would have f(x) as their derivative. The result…
Integration Using a Table of Anti-Derivatives
Integration may be regarded as the reverse of differentiation, so a table of derivatives can be read backwards as a table of anti-derivatives. The final result for an indefinite integral…
Integration by Parts
A special rule, integration by parts, can often be used to integrate the product of two functions. It is appropriate when one of the functions forming the product is recognised…
Integration by Substitution
There are occasions when it is possible to perform an apparently difficult piece of integration by first making a substitution. This has the effect of changing the variable and the…
Integrating Algebraic Fractions Part 1
The integral of an algebraic fraction can often be found by first expressing the fraction as the sum of its partial fractions. To do this it is necessary to draw…
Integrating Algebraic Fractions Part 2
The integral of an algebraic fraction can often be found by first expressing the fraction as the sum of its partial fractions. Further techniques are available when the denominator involves…
Integration Using Trigonometric Formulae
Sometimes integrals involving trigonometric functions can be evaluated by using trigonometric identities. These allow the integrand to be written in an alternative form which may be more amenable to integration.…
Finding Areas by Integration
In simple cases, areas can be found by evaluating a single definite integral. Sometimes the integral gives a negative answer, and sometimes the correct answer can be obtained only by…
Volumes of Solids of Revolution
A solid of revolution is obtained by rotating a curve about the x-axis. There is a straightforward technique, using integration, which enables us to calculate the volume of such a…
Integration Leading to Log Functions
The derivative of x is 1/x. As a consequence, if we reverse the process, the integral of 1/x is ln x + c. In this unit we generalise this result…

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