C2 Chapter 11: Integration Dr J Frost

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C2 Chapter 11: Integration Dr J Frost (jfrosttiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 1st September 2015 ? ? ? ? ? We could add together the area of individual strips, which we want to make as thin as possible

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C2 Chapter 11: Integration Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com Last modified: 1st September 2015

? ? ? ? ?

We could add together the area of individual strips, which we want to make as thin as possible…

 Reflecting on above, do you think the following definite integrals would be positive or negative or 0?   + 0    + 0    + 0

? ? ?

? ? Bro Tip: Be careful with your negatives, and use bracketing to avoid errors.

1 2 4 6 a c e ? ? ? ? ? ?

Sketch:
(Hint: factorise!) ? ? ?

-3 1 The Sketch The number crunching ? ?

1 2 3 4 5 ? ? ? ? ?

How could we use a similar principle if we were looking for the area bound between two lines? ? therefore area… ?

Bro Tip: We’ll need to find the points at which they intersect. ?

Edexcel C2 May 2013 (Retracted) ? ?

y = x(x-3) y = 2x A B C Bro Tip: Sometimes we can subtract areas from others. e.g. Here we could start with the area of the triangle OBC. ?

1 3 4 9 ? ? ? ?

(Probably more difficult than you’d see in an exam paper, but you never know…) Q6 7 7 ?

Instead of infinitely thin rectangular strips, we might use trapeziums to approximate the area under the curve.

What is the area here? ?

In general: width of each trapezium Area under curve is approximately ? Example ?

0.8571 ? ? May 2013 (Retracted)

To add: When do we underestimate and overestimate?

C2 Chapter 11: Integration Dr J Frost

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