The 11 videos in this collection focus on all aspects of Integration, from integration as summation to integration leading to log functions.

Running Time

341 mins

Nb videos

11 videos included

Kanopy ID

1106025

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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…

Moving Bodies with Constant Mass

A compilation of the following programs: : Deceleration with parachutes, Acceleration with planes, Bows and Arrows, Differentiation of natural log of x (tutorial), Inverse Trig function - differentiation (tutorial), Exponential Functions (tutorial), Integrals that lead to log functions (tutorial), Integration by substitution (tutorial), Partial Fractions (tutorial) and Differential Equations -…

Integration By Partial Fractions

This program covers the important topic of Integration by Partial Fractions in Calculus. We begin by discussing what a Partial Fraction is, how it can be used to solve integrals, and why it is a central topic in Calculus. Next, we solve several practical calculus problems that give students practice…

Functions and Graphs

The 8 videos in this collection focus on all aspects of Functions and Graphs.

Algebra

The 18 videos in this collection focus on all aspects of Algebra, from logarithms to quadratic equations and partial fractions.

Moving Bodies with Variable Mass

A compilation of the following programs: Impluse, Rockets and Avalanches, Integrals that lead to log functions (tutorial) and Differential Equations - variables separable (tutorial)

Arithmetic

The 8 videos in this collection focus on all aspects of Arithmetic, from fractions to percentages and ratios.

Differentiation

The 14 videos in this collection focus on all aspects of Differentiation, from maxima and minima to the chain, product and quotient rule.

Sequences and Series

The 5 videos in this collection focus on all aspects of Sequences and Series.

Moments

A compilation of the following programs: Doors, heart valves & flic-flacs, Circular Motion, Modelling forces - sliding and toppling, Differentiation of vectors - radial and transverse components (tutorial), Differentiation of Vectors (tutorial) and Combining vectors pt 2 (tutorial).

Vectors

A compilation of the following programs: Kites, Angular Momentum, Vectors and Moments, Modelling with 3D vectors, Introduction to Vectors (tutorial), Cartesian representation of vectors in 3D space (tutorial), Combining vectors pt 1 and 2 (tutorials) and Differentiation of vectors (tutorial).

Trigonometry

The 11 videos in this collection focus on all aspects of Trigonometry, from Pythagoras' theorem to cosec, sec and cot.

The Joy of Integral Calculus

Geometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities.

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