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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)
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Starter: 1) 2)
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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
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Key words: Bounded finite Region
Real life Key words: Bounded finite Region
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Use the general rule above to work out the definite integral
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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)*
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Questions Red I can integrate simple functions between defined limits
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Questions Amber I can use definite integration to find areas under curves
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Questions Amber I can use definite integration to find areas under curves
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What is the correct answer?
Find What is the correct answer? 6 14 20
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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
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Questions Green I can work out areas of curves under the x-axis
*(Sketch graphs and show where curve intersects x-axis)*
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Questions Green I can work out areas of curves under the x-axis
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What is the correct answer?
2.5 4.5 8.5
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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
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Competition Boys vs Girls
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Best out of 3 Question 1 Find
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Best out of 3 Question 2 Find the area between the curve , the x-axis and the x = 2 and x = 3. B
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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 )
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Question 3 Shaded area = area of rectangle – area under curve
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Bonus Find So,
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Homework Year 12 Core 2 23. Integration Q1 - 6
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