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



b)

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