LCHL Integration

Integration Presentation

Integration Notes & Worksheet

These lessons will involve the students in investigating and understanding:

 That anti-differentiation is the reverse process of differentiation.

 How to find the anti-derivative F(x) of function ݂f(x)

 That the indefinite anti-derivative is the set of all possible antiderivatives of a function

 That a distinct anti-derivative is one element of this set which satisfies some initial condition

 That the process of finding the area between a curve and the x -axis (or y– axis) over an interval on the axis, is known as integration

 That the area between a function and the x-axis over an interval may be calculated using the limit of the sum of the areas of rectangles, as the number of rectangles tends to infinity and the width of each rectangle tends to zero.

 That the area A between the graph of ݂f(x) and the x-axis over the interval from [a,b] is :

 The area beneath a function f(x) from a to b is given by:

 The antiderivative is usually called the indefinite integral

 The indefinite integral, of ݂f(x) is a set of functions equal to the set of all the antiderivatives of f(x). They differ by a constant C.

 The definite integral with limits a to b is a number equal to the net signed area between the graph of ݂f(x) and the interval [a,b]

 That integration is the reverse process of differentiation (anti - differentiation)

 How to integrate sums, differences and constant multiples of functions of the form , where,

• • x^a , a E Q

  • a^x , a E R, a>0

  • sin ax , a E R

  • cos ax , a E R

 How to determine areas of plane regions bounded by polynomial and exponential functions

 How to use integration to find the average value of a function over an interval