C1 Chapter 8 Integration Dr J Frost Last modified: 14 th November 2013

This constant would disappear when we differentiate. Because we don’t know the exact function, we call it indefinite integration. ? ? ? ? We increase the index by one first, then divide by it. The opposite of differentiation We know how to differentiate. Sometimes we want to know the original function given the gradient. This is known as integration.

Get it the right way round! The ‘classic mistake’ is to get differentiation and integration mixed up. Remember for differentiation, you multiply first, whereas for integration you change the power first (then divide!). ? ? ? ?

Exercises Q ? ? ? ? ? ? ? ? ? ?

New notation! Integrate… ? ? ?

Further Examples ? Notice that at this point, we haven’t actually integrated yet, only simplified, hence the integral symbol remains! ?

Exercises Exercise 8B Exercise 8D Exercise 8C ? ? ? ? ? ? ? ? ? ? ?

Working out the c

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Exercise 8E Find the equation of the curve when the gradient and a point on the line are the following: 1a ? ? ?

Schoolboy Errors TM What’s wrong with these workings? They’ve integrated on the second line, so they don’t want the integral symbol! ? ?