Area between Parabolas - Mr Barton Maths

Area between Parabolas () () Whats the area bounded by these parabolas? Let the functions be: Where do they intersect?

Notice that these values are independent of , and . The area we require is given by: ( ) + () We only need to evaluate: ()

( ) + despite part of its area being below the x-axis and therefore negative. Imagine both curves translated by the vector . The area wouldnt change and we would have no negative areas. So what does -

() () look like? So what does - () ()

look like? 1 2 = [ ( ) +( )] 1 A

B C D E F G H

I J K L M N

O P Note to Teacher In all cases is divisible by to make it easier for you to check an answer. Resources Area between Parabolas Whats the area

bounded by these parabolas? Not accurately drawn SIC_24 A Area between Parabolas Whats the area bounded by these

parabolas? Not accurately drawn SIC_24 B Area between Parabolas Whats the area bounded by these parabolas?

Not accurately drawn SIC_24 C Area between Parabolas Whats the area bounded by these parabolas?

Not accurately drawn SIC_24 D Area between Parabolas Whats the area bounded by these parabolas? Not accurately drawn

SIC_24 E Area between Parabolas Whats the area bounded by these parabolas? Not accurately drawn

F SIC_24 Area between Parabolas Whats the area bounded by these parabolas? Not accurately drawn G SIC_24

Area between Parabolas Whats the area bounded by these parabolas? Not accurately drawn H SIC_24 Area between

Parabolas Whats the area bounded by these parabolas? Not accurately drawn SIC_24 I Area between Parabolas

Whats the area bounded by these parabolas? Not accurately drawn SIC_24 J Area between Parabolas Whats the area

bounded by these parabolas? Not accurately drawn SIC_24 K Area between Parabolas Whats the area bounded by these

parabolas? Not accurately drawn SIC_24 L Area between Parabolas Whats the area bounded by these parabolas?

Not accurately drawn SIC_24 M Area between Parabolas Whats the area bounded by these parabolas?

Not accurately drawn N SIC_24 Area between Parabolas Whats the area bounded by these parabolas? Not accurately drawn

O SIC_24 Area between Parabolas Whats the area bounded by these parabolas? Not accurately drawn SIC_24

P What is the area bounded by these curves? A What is the area bounded by these curves? SIC_24 What is the area bounded by these

curves? B E SIC_24 What is the area bounded by these curves? SIC_24

What is the area bounded by these curves? F SIC_24 What is the area bounded by these curves? SIC_24 SIC_24

C G What is the area bounded by these curves? What is the area bounded by these curves? SIC_24 SIC_24

What is the area bounded by these curves? I What is the area bounded by these curves? SIC_24 What is the area bounded by these curves?

J M SIC_24 What is the area bounded by these curves? SIC_24 What is the area bounded by these

curves? N SIC_24 What is the area bounded by these curves? SIC_24 SIC_24

K O What is the area bounded by these curves? What is the area bounded by these curves? SIC_24 SIC_24

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