Showing posts from June, 2010

Differentiation of Trig functions Part II

Differentiation of trig functions using Chain rule, Product rule and Quotient rule

Example 1

Technique: Use of Chain rule

Example 2
Given that , show that

Technique: use Quotient Rule

What's next ?
Check out other topics in Contents Page
Revise the basics of the differentiation of trig functions

Differentiation and Integration of Trigonometric functions

A lot of students confuse the differentiation of trig functions with the integration of trig functions

The most effective way is to study them together

Remember that:

We can differentiate tan x but we cannot integrate tan x

Example 1

Example 2

Note that

Example 3

Example 4

Note that

Surds, Log and Indices

An interesting question showing these 3 topics can be tested in a single question


Express as

i) Hence show that

ii) Given that , prove that

Techniques tested

Rationalization Indices: Power Law:


Technique used: Rationalization

Techniques used:
Power Law:

From LHS


This part of the question requires us to use the Substitution technique

Using the quadratic formula,

Recall that


Technique used: Taking log on both sides

Recall that in part (i) we showed that

Interesting question, dont you think ?

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For a revision of surds, click here
For a revision of logarithms, click here
For a revision of indices, click here

Integration Techniques Part II

"Anti Chain Rule"

This isnt an official maths term. Just something to help students remember how this technique is applied

Recall the use of chain rule in differentiation

Differentiate with respect to x

Chain rule: "Bring down power, negate power by one multiply by the differentiation of the terms within the brackets"

Integration using "Anti Chain rule":
Increase power by one, divided by new power and the differentiation of the terms within the brackets"

Question 1

Note that there are some limitations to "anti chain rule" You cannot . "Anti chain rule" is ony possible with linear factors

Question 2

Integration as anti differentiation

In question 1,

when we differentiate y, we get

When we integrate , we get back

Question 3

Given that

a) Find

b) Hence evaluate


Integration techniques Part I

Integrating term by term


where c is a constant

Example 1

Example 2

Example 3

Example 4