Integration

__**Integration **__ In the early history of calculus there were two fundamental problems: the gradient of the tangent to a curve at a point (differentiation), and the calculation of the area of a region under a curve. This process has been referred to as anti-differentiation or the primitive function, but it is also known as integration. The area of figures which involve curves, such as an area of land where one side meets a river, can be calculated using integration.

__**Lesson 1 - Riemann Sums **__ Open the file below to investigate how non-geometric areas can be estimated using rectangles before attempting Exercise 18.1 

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__**Lesson 2 - The Definite Integral **__ Open this file and save it to your laptop for the lesson notes on Exercise 18.2 

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__**Lesson 3 - The Indefinite Integral **__ Open this file and save it to your laptop for the lesson notes on Exercise 18.3 

Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Integration

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 4 - Reverse Chain Rule **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.4 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Further Integration

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 5 - Further Definite Integrals **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.5 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Equation Of A Curve Given Its Derivative

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 6 - Further Areas **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.6 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Areas Enclosed By The x-Axis

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 7 - Area Related To The y-Axis **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.7 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Areas Enclosed By The y-Axis

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 8 - Area Between Two Curves **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.8 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Area Between Curves

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 9 - Trapezoidal Rule **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open the file below to investigate how to approximate the area under a curve using trapezia. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;"> Watch this tutorial from MathsOnline.Miscellaneous Integration Involving Areas

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 10 - Simpson's Rule **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.10 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;"> <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Simpson's Rule & Trapezoidal Rule

__**<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Lesson 11 - Volumes of Revolution **__ <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Open this file and save it to your laptop for the lesson notes on Exercise 18.11 <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;"> <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Watch this tutorial from MathsOnline. <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 150%; text-align: center;">Volumes of Revolution <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 20px; text-align: center;">