C2 – Integration – Chapter 11

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Presentation transcript:

C2 – Integration – Chapter 11 24/11/2018 L O: ( Look at the steps to success ) To explore definite integration and its application to finding areas Starter: 1) 2)

Starter: 1) 2)

Steps to success             Red Amber I can integrate simple functions between defined limits I can use definite integration to find areas under curves       Green Challenge I can work out areas of curves under the x-axis I can work out areas between a curve and a straight line      

Key words: Bounded finite Region Real life Key words: Bounded finite Region

Use the general rule above to work out the definite integral

Questions Red I can integrate simple functions between defined limits Amber I can use definite integration to find areas under curves *(Sketch graphs and show where curve intersects x-axis)*

Questions Red I can integrate simple functions between defined limits

Questions Amber I can use definite integration to find areas under curves

Questions Amber I can use definite integration to find areas under curves

What is the correct answer? Find What is the correct answer? 6 14 20

Steps to success             Red Amber I can integrate simple functions between defined limits I can use definite integration to find areas under curves       Green Challenge I can work out areas of curves under the x-axis I can work out areas between a curve and a straight line      

Questions Green I can work out areas of curves under the x-axis *(Sketch graphs and show where curve intersects x-axis)*

Questions Green I can work out areas of curves under the x-axis

What is the correct answer? 2.5 4.5 8.5

Summary The method for evaluating the definite integral is: Find the indefinite integral but omit C Draw square brackets and hang the limits on the end Replace x with the top limit the bottom limit Subtract and evaluate

Competition Boys vs Girls

Best out of 3 Question 1 Find

Best out of 3 Question 2 Find the area between the curve , the x-axis and the x = 2 and x = 3. B

Best out of 3 Question 3 Find the points of intersection of the following curves and lines. Show the graphs in a sketch, shade the region bounded by the graphs and find its area. (a) ; Solution: (a) ( y = 6 for both points )

Question 3 Shaded area = area of rectangle – area under curve

Bonus Find So,

Homework www.fevmaths.com Year 12 Core 2 23. Integration Q1 - 6