Areas of Compound Regions (HSC SSCE Mathematics Advanced): Flashcards
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Practise the cards
10 cards from this deck
Process of breaking compound regions into sections
Process of breaking compound regions into sections
Dissection
Area between curves where
Area between curves where
Simple rule for area between curves
Simple rule for area between curves
Integrate (top curve minus bottom curve)
Critical condition for area formula
Critical condition for area formula
Curves don't cross within the interval
Action when curves cross in interval
Action when curves cross in interval
Calculate separate integrals for each section
Does formula work if region crosses -axis?
Does formula work if region crosses -axis?
Yes, no need to treat above/below separately
How to find exact intersection points
How to find exact intersection points
Solve algebraically by setting equations equal
Different curves bound different parts of -axis
Different curves bound different parts of -axis
Calculate each section separately, then add
Why sketch the region first?
Why sketch the region first?
Identify boundaries, intersections, which curve is on top
Result if curves cross but calculation not split
Result if curves cross but calculation not split
Areas cancel out, giving incorrect result